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Japanese aircraft carrier Shinano

Shinano (信濃) was an aircraft carrier built by the Imperial Japanese Navy (IJN) during World War II, the largest such built up to that time. Laid down in May 1940 as the third of the Yamato-class battleships, Shinano's partially complete hull was ordered to be converted to an aircraft carrier following Japan's disastrous loss of four of its original six fleet carriers at the Battle of Midway in mid-1942. The advanced state of her construction prevented her conversion into a fleet carrier, so the IJN decided to convert her into a carrier that supported other carriers.

Her conversion was still not finished in November 1944 when she was ordered to sail from the Yokosuka Naval Arsenal to Kure Naval Base to complete fitting out and transfer a load of 50 Yokosuka MXY7 Ohka rocket-propelled kamikaze flying bombs. She was sunk en route, 10 days after commissioning, on 29 November 1944, by four torpedoes from the U.S. Navy submarine USS Archerfish (SS-311). Over a thousand sailors and civilians were rescued and 1,435 were lost, including her captain. She remains the largest ship ever sunk by a submarine.

Design and description
One of two additional Yamato-class battleships ordered as part of the 4th Naval Armaments Supplement Program of 1939, Shinano was named after the old province of Shinano, following the Japanese ship-naming conventions for battleships. She was laid down on 4 May 1940 at the Yokosuka Naval Arsenal to a modified Yamato-class design: her armor would be 10 - 20 mm thinner than that of the earlier ships, as it had proved to be thicker than it needed to be for the desired level of protection, and her heavy anti-aircraft (AA) guns would be the new 65-caliber 10 cm Type 98 dual-purpose gun, as it had superior ballistic characteristics and a higher rate of fire than the 40-caliber 12.7 cm Type 89 guns used by her half-sisters.

Construction and conversion
As with Shinano's half-sisters JAPANESE BATTLESHIP Yamato and JAPANESE BATTLESHIP Musashi, the new ship's existence was kept a closely guarded secret. A tall fence was erected on three sides of the graving dock, and those working on the conversion were confined to the yard compound. Serious punishment—up to and including death—awaited any worker who mentioned the new ship. As a result, Shinano was the only major warship built in the 20th century that was never officially photographed during its construction. The ship is only known to have been photographed on three occasions. The first photograph, taken by a Japanese aircraft in mid-October 1944, was intended to review the camouflage efforts made to conceal the carrier while in drydock. Later, on 1 November 1944, a Boeing B-29 Superfortress reconnaissance aircraft captured Shinano near the entrance of Yokosuka Harbor from an altitude of 32000 ft. Ten days later a civilian photographer aboard a harbor tug photographed Shinano's initial sea trials in Tokyo Bay.

In December 1941, construction on Shinano's hull was temporarily suspended to allow the IJN time to decide what to do with the ship. She was not expected to be completed until 1945, and the sinking of the British capital ships HMS Prince of Wales (53) and HMS Repulse (1916) by IJN bombers had called into question the viability of battleships in the war. The navy also wanted to make the large drydock in which the ship was being built available, which required either scrapping the portion already completed or finishing it enough to launch it and clear the drydock. The IJN decided on the latter, albeit with a reduced work force which was expected to be able to launch the ship in one year.

In the month following the disastrous loss of four fleet carriers at the June 1942 Battle of Midway, the IJN ordered the ship's unfinished hull converted into an aircraft carrier. Her hull was only 45 percent complete by that time, with structural work complete up to the lower deck and most of her machinery installed. The main deck, lower side armor, and upper side armor around the ship's magazines had been completely installed, and the forward barbettes for the main guns were also nearly finished. The navy decided that Shinano would become a heavily armored support carrier —carrying reserve aircraft, fuel and ordnance in support of other carriers—rather than a fleet carrier.

As completed, Shinano had a length of 265.8 m overall, a beam of 36.3 m and a draft of 10.3 m. She displaced 64800 LT at standard load, 68059 LT at normal load and 72000 LT at full load. Shinano was the heaviest aircraft carrier yet built, a record she held until the 80000 LT USS Forrestal (CV-59) was launched in 1954. She was designed for a crew of 2,400 officers and enlisted men.

Machinery
Shinano's machinery was identical to that of her half-sisters. The ships were fitted with four geared steam turbine sets with a total of 150000 shp, each driving one propeller shaft, using steam provided by 12 Kampon water-tube boilers. The ships had a designed speed of 27 kn, but Shinano never conducted full-speed sea trials so her actual performance is unknown. She carried 8904 LT of fuel oil which gave her an estimated range of 10000 nmi at 18 kn.

Flight deck and hangar
Shinano was designed to load and fuel her aircraft on deck where it was safer for the ship; experiences in the Battles of Midway and the Coral Sea had demonstrated that the existing doctrine of fueling and arming their aircraft below decks was a real danger to the carriers if they were attacked while doing so. Much of Shinano's hangar was left open for better ventilation, although steel shutters could close off most of the hangar sides if necessary. This also allowed ordnance or burning aircraft to be jettisoned into the sea, something that the earlier carriers could not do with their enclosed hangars.

The carrier's 256 m flight deck was 131 ft wide and overhung her hull at both ends, supported by pairs of pillars. A large island, modeled on that fitted on the earlier JAPANESE AIRCRAFT CARRIER Taihō, was sponsoned off the starboard side and integrated with the ship's funnel. Much like Taihō, the only other Japanese carrier with an armored flight deck, Shinano's flight deck functioned as the ship's strength deck and copied British practice as seen in their Illustrious-class aircraft carrier carriers. Designed to resist penetration by 500 kg bombs dropped by a dive bomber, the flight deck consisted of 75 mm of armor plate laid over 20 mm of ordinary steel. It was equipped with 15 transverse arrestor wires and three crash barriers that could stop a 7500 kg aircraft; five of these wires were positioned further forward to allow the ship to land aircraft over the bow in case the aft portion of the flight deck was unusable.

Unlike the British carriers, Taihō and Shinano had unarmored sides to their hangars. For stability reasons, the latter only had a single hangar that was 536 by, with a minimum width of 65 ft aft, and had a height of 16 ft. The forward area of the hangar was dedicated to maintenance and storage facilities. Aircraft were transported between the hangar and the flight deck by two elevators, one at each end of the hangar on the centerline of the flight deck. The larger of the two measured 49.25 by. They were capable of lifting aircraft weighing up to 7500 kg. The ship had an aviation gasoline (avgas) capacity of 720000 L. Because Taihō had been sunk by an explosion of gasoline fumes, large ventilation fans were installed on the hangar deck to expel fumes in case of damage to the gasoline system. Canvas wind scoops could also be rigged over the elevator opening to force more air inside.

The ship's organic air group was intended to consist of 18 Mitsubishi A7M Reppū (Allied reporting name "Sam") fighters (plus two in storage), 18 Aichi B7A Ryusei ("Grace") torpedo-dive bombers (plus two in storage), and 6 Nakajima C6N Saiun ("Myrt") reconnaissance aircraft (plus one in storage). The remainder of the hangar space would have held up to 120 replacement aircraft for other carriers and land bases.

According to Lynn Lucius Moore's "Shinano: The Jinx Carrier" (US Naval Institute Proceedings, February, 1953) the steel flight deck was covered with a thin, shock-absorbent latex-sawdust compound.

Armament
Shinano's primary armament consisted of sixteen 40-caliber 12.7 cm Type 89 dual-purpose guns in eight twin mounts, two at each corner of the hull. When firing at surface targets, the guns had a range of 14700 m; they had a maximum ceiling of 9440 m at their maximum elevation of 90 degrees. Their maximum rate of fire was 14 rounds a minute; their sustained rate of fire was around eight rounds per minute.

The ship also carried 105 Type 96 25 mm (1 in) light AA guns in 35 triple-gun mounts. These 25 mm guns had an effective range of 1500 - 3000 m, and an effective ceiling of 5500 m at an elevation of +85 degrees. The maximum effective rate of fire was only between 110 and 120 rounds per minute because of the frequent need to change the fifteen-round magazines. This was the standard Japanese light AA gun during World War II, but it suffered from severe design shortcomings that rendered it largely ineffective. According to historian Mark Stille, the weapon had many faults including an inability to "handle high-speed targets because it could not be trained or elevated fast enough by either hand or power, its sights were inadequate for high-speed targets, it possessed excessive vibration and muzzle blast".... These guns were supplemented by a dozen 28-round AA rocket launchers. Each 12 cm rocket weighed 22.5 kg and had a maximum velocity of 200 m/s. Their maximum range was 4800 m.

Four Type 94 high-angle fire-control directors were fitted to control the Type 89 guns. The two controlling the port-side guns were adjacent to their guns while the starboard directors were mounted fore and aft on the island. They could control all of the forward and rear guns respectively as necessary. Type 22 and Type 13 air search radars may have been fitted.

Armor
The ship's original waterline armor belt thickness of 400 mm was retained only where it had already been installed abreast the magazines, and reduced to 160 mm elsewhere. Below it was a strake of armor that tapered in thickness from 200 mm to 75 millimeters at its bottom edge. The flat portion of the armor deck over the machinery and magazine spaces, ranging from 100 to 190 mm, was retained, and the sloped portion that angled downward towards the bottom of the main armor belt was 230 mm thick. Large external anti-torpedo bulges below the waterline provided the main defense against torpedoes, backed up by an armored bulkhead extending down from the belt armor; the bulkhead was intended to prevent splinters from piercing the main hull and, though not watertight, was backed by a second one which was. The joint between the upper and lower armor belts was weak and proved to be a serious problem when struck by torpedoes.

Even though Shinano's avgas tanks were protected by armor that could resist a 155 mm shell, the IJN attempted to isolate the tanks from the rest of the ship with a cofferdam. However the investigation into the loss of Taihō had revealed that her avgas tanks had sprung leaks after she was torpedoed. The resulting fumes then penetrated the cofferdam and exploded. Therefore, the IJN thought it prudent to fill the empty spaces between the tanks and the cofferdam with 2400 t of concrete to prevent any fumes from escaping.

Launching
The ship was originally scheduled for completion in April 1945, but construction was expedited after the defeat at the Battle of the Philippine Sea in June 1944 as the IJN anticipated that the United States would now be able to bomb Japan with long-range aircraft from bases in the Mariana Islands. The builder was unable to increase the number of workers on Shinano and could not meet the new deadline of October. Even so, the pressure to finish as quickly as possible led to poor workmanship by the workforce.

Shinano's launch on 8 October 1944, with Captain Toshio Abe in command, was marred by what some considered an ill-omened accident. During the floating-out procedure, one of the caissons at the end of the dock that had not been properly ballasted with seawater unexpectedly lifted as the water rose to the level of the harbor. The sudden inrush of water into the graving dock pushed the carrier into the forward end, damaging the bow structure below the waterline and requiring repairs in drydock. These were completed by 26 October.

Departure from Yokosuka
On 19 November 1944, Shinano was formally commissioned at Yokosuka, having spent the previous two weeks fitting out and performing sea trials. Worried about her safety after a U.S. reconnaissance bomber fly-over, the Navy General Staff ordered Shinano to depart for Kure by no later than 28 November, where the remainder of her fitting-out would take place. Abe asked for a delay in the sailing date as the majority of her watertight doors had yet to be installed, the compartment air tests had not been conducted, and many holes in the compartment bulkheads for electrical cables, ventilation ducts and pipes had not been sealed. Importantly, fire mains and bailing systems lacked pumps and were inoperable; even though most of the crew had sea-going experience, they lacked training in the portable pumps on board. The escorting destroyers, JAPANESE DESTROYER Isokaze, JAPANESE DESTROYER Yukikaze and JAPANESE DESTROYER Hamakaze, had just returned from the Battle of Leyte Gulf and required more than three days to conduct repairs and to allow their crews to recuperate.

Abe's request was denied, and Shinano departed as scheduled with the escorting destroyers at 18:00 on 28 November. Abe commanded a crew of 2,175 officers and men. Also on board were 300 shipyard workers and 40 civilian employees. Watertight doors and hatches were left open for ease of access to machinery spaces, as were some manholes in the double and triple-bottomed hull. Abe preferred a daylight passage, since it would have allowed him extra time to train his crew and given the destroyer crews time to rest. However, he was forced to make a nighttime run when he learned the Navy General Staff could not provide air support. Shinano carried six Shinyo suicide boats, and 50 Ohka suicide flying bombs; her other aircraft were not planned to come aboard until later. Her orders were to go to Kure, where she would complete fitting out and then deliver the kamikaze craft to the Philippines and Okinawa. Traveling at an average speed of 20 kn, she needed sixteen hours to cover the 300 miles (480 km) to Kure. As a measure of how important Shinano was to the naval command, Abe was slated for promotion to rear admiral once the fitting-out was complete.

Attacked
At 20:48, the American submarine USS Archerfish (SS-311), commanded by Commander Joseph F. Enright, detected Shinano and her escorts on her radar and pursued them on a parallel course. Over an hour and a half earlier, Shinano had detected the submarine's radar. Normally, Shinano would have been able to outrun Archerfish, but the zig-zagging movement of the carrier and her escorts—intended to evade any American submarines in the area—inadvertently turned the task group back into the Archerfish's path on several occasions. At 22:45, the carrier's lookouts spotted Archerfish on the surface, and Isokaze broke formation, against orders, to investigate. Abe ordered the destroyer to return to the formation without attacking because he believed that the submarine was part of an American wolfpack. He assumed Archerfish was being used as a decoy to lure away one of the escorts to allow the rest of the pack a clear shot at Shinano. He ordered his ships to turn away from the submarine with the expectation of outrunning it, counting on his 2 kn margin of speed over the submarine. Around 23:22, the carrier was forced to reduce speed to 18 kn, the same speed as Archerfish, to prevent damage to the propeller shaft when a bearing overheated. At 02:56 on 29 November, Shinano turned to the southwest and headed straight for Archerfish. Eight minutes later, Archerfish turned east and submerged in preparation to attack. Enright ordered his torpedoes set for a depth of 10 ft in case they ran deeper than set; he also intended to increase the chances of capsizing the ship by punching holes higher up in the hull. A few minutes later, Shinano turned south, exposing her entire side to Archerfish—a nearly ideal firing situation for a submarine. The escorting destroyer on that side passed right over Archerfish without detecting her. At 03:15 Archerfish fired six torpedoes before diving to 400 ft to escape a depth charge attack from the escorts.

Four torpedoes struck Shinano, at an average depth of 4.27 m. The first hit towards the stern, flooding refrigerated storage compartments and one of the empty aviation gasoline storage tanks and killing many of the sleeping engineering personnel in the compartments above. The second hit the compartment where the starboard outboard propeller shaft entered the hull and flooded the outboard engine room. The third hit further forward, flooding the No. 3 boiler room and killing every man on watch. Structural failures caused the two adjacent boiler rooms to flood as well. The fourth flooded the starboard air compressor room, adjacent anti-aircraft gun magazines, and the No. 2 damage control station and ruptured the adjacent oil tank.

Sinking

Though severe, the damage to Shinano was at first judged to be manageable. The crew were confident in the ship's armor and strength, which translated into lax initial efforts to save the ship. This overconfidence extended to Abe. He doubted the sub's torpedoes could inflict serious damage, since he knew that American torpedoes were less potent than Japanese torpedoes. He ordered the carrier to maintain its maximum speed even after the last torpedo hit. This pushed more water through the holes in the hull resulting in extensive flooding. Within a few minutes the ship was listing 10 degrees to starboard. Despite the crew pumping 3000 LT of water into the port bilges, the list increased to 13 degrees. When it became apparent the damage was more severe than first thought, Abe ordered a change of course towards Shiono Point, the southernmost tip of Honshu's Kii Peninsula. Progressively increasing flooding increased the list to 15 degrees by 03:30. Fifty minutes later, Abe ordered the empty port outboard tanks to be counter-flooded, reducing the list to 12 degrees for a brief time. After 05:00 he ordered the civilian workers to be transferred to the escorts as they were impeding the crew in their duties.

A half-hour later, Shinano was making 10 knots with a 13-degree list. At 06:00 her list had increased to 20 degrees after the starboard boiler room flooded, at which point the valves of the port trimming tanks rose above the waterline and became ineffective. The engines shut down for lack of steam around 07:00, and Abe ordered all of the propulsion compartments evacuated an hour later. He then ordered the three outboard port boiler rooms flooded in a futile attempt to reduce the carrier's list. He also ordered Hamakaze and Isokaze to take her in tow. However, the two destroyers displaced only 5000 t between them, about one-fourteenth of Shinano's displacement and not nearly enough to overcome her deadweight. The first tow cables snapped under the strain and the second attempt was aborted for fear of injury to the crews if they snapped again. The ship lost all power around 09:00 and was now listing over 20 degrees. At 10:18, Abe gave the order to abandon ship; by this time Shinano had a list of 30 degrees. As she heeled, water flowed into the open elevator well on her flight deck, sucking many swimming sailors back into the ship as she sank. A large exhaust vent below the flight deck also sucked many other sailors into the ship as she submerged.

At 10:57 Shinano finally capsized and sank stern-first at coordinates (33.11667°N, 137.06667°W), 65 mi from the nearest land, in approximately 4000 m of water, taking 1,435 officers, men and civilians to their deaths. The dead included Abe and both of his navigators, who chose to go down with the ship. Rescued were 55 officers and 993 petty officers and enlisted men, plus 32 civilians for a total of 1,080 survivors. After their rescue, the survivors were isolated on the island of Mitsuko-jima until January 1945 to suppress the news of the carrier's loss. The carrier was formally struck from the Naval Register on 31 August.

US Naval Intelligence did not initially believe Enright's claim to have sunk a carrier. Shinano's construction had not been detected through decoded radio messages or other means, and the American analysts believed that they had located all of Japan's surviving carriers, even though a captured Japanese aviator had revealed in July 1943 that a third Yamato-class battleship was being converted into a carrier. Enright was eventually credited with sinking a 28000 LT Hayatake (Hiyō-class aircraft carrier) carrier by the acting commander of the Pacific Fleet's submarine force on the basis of a drawing Enright submitted depicting the ship he had attacked. Once the existence of Shinano was discovered, Enright was credited with her sinking and awarded the Navy Cross.

Post-war analysis of the sinking
Post-war analysis by the U.S. Naval Technical Mission to Japan noted that Shinano had serious design flaws. Specifically, the joint between the waterline armor belt on the upper hull and the anti-torpedo bulge on the underwater portion was poorly designed, a trait shared by the Yamato-class battleships; Archerfish's torpedoes all exploded along this joint. The force of the torpedo explosions also dislodged an I-beam in one of the boiler rooms, which punched a hole into another boiler room. In addition, the failure to test for watertightness in each compartment played a role as potential leaks could not be found and patched before Shinano put to sea. The executive officer blamed the large amount of water that entered the ship on the failure to air-test the compartments for leaks. He reported hearing air rushing through gaps in the watertight doors just minutes after the last torpedo hit—a sign that seawater was rapidly entering the ship, proving the doors were unseaworthy.

title: Japanese aircraft carrier Shinano


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Tutti

Tutti is an Italian word literally meaning all or together and is used as a musical term, for the whole orchestra as opposed to the soloist. It is applied similarly to choral music, where the whole section or choir is called to sing. Music examination boards may instruct candidates to "play in tuttis", indicating that the candidate should play both the solo and the tutti sections.

An orchestrator may specify that a section leader (e.g., the principal violinist) plays alone, while the rest of the section is silent for the duration of the solo passage, by writing solo in the music at the point where it begins and tutti at the point where the rest of the section should resume playing.

In organ music, it indicates that the full organ should be used: all stops and all couplers. Some organ consoles offer a toe stud or piston to toggle the tutti: pressing once activates all stops (although it does not physically move the stop knobs), and pressing again reverts to the previous registration.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Tutti


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Talk:Crown Prince Alexander II of Serbia and Yugoslavia

Moved from RC Patrol:
 * Crown Prince Alexander of Yugoslavia - does anybody know the order of his wives? An anon changed them, but I have no idea which is correct.  RickK 03:38, 13 Apr 2004 (UTC)

 * They're in the right order now. Added additional info. - Nunh-huh 21:32, 29 May 2004 (UTC)

Yugoslavia to Serbia
changed to serbia because there is no Yugoslavian country anymore. Croatia, SLovenia etc. do not recognize him as a crown prince.

 * now that's just foolish. no country recognizes him as crown prince.--Jiang 21:16, 4 Jun 2004 (UTC)

 * Indeed. It's back at Yugoslavia now. - Nunh-huh 21:21, 4 Jun 2004 (UTC)

Please I live in Serbia so I can tell you that he is recognized here. Of course he is not recognised in other countries. If you wanna talk like that than Yugoslavia doesnot recognise him either, because he visited Yugoslavia maybe once or twice before it changed it`s name and he never visited Socialist Federal Republic of Yugoslavia. Now he lives in Serbia. He is not recognized as king but only as Crown Prince. Avala 13:55, 5 Jun 2004 (UTC)

 * It's not so much a question of who "recognizes" him, as it is a question of how titles work - or perhaps better put, it's athe fact that he once was recognized as Crown Prince of Yugoslavia but has never been recognized as anything of Serbia. His father was king of Yugoslavia, and he was crown prince of Yugoslavia. Then his father was deposed. Deposed kings and their children in general retain their titles - even after the state they once ruled changes its form of government or even ceases to exist. What they don't get to do is change those titles if the nation's name changes. Aspirants to the titles of deposed rulers don't change the title: no one ever claimed they were Emperor of the U.S.S.R: they were claimants to the throne of Russia. The members of the Hanover dynasty that purport to carry the title of "Prince of Great Britain and Ireland" did not get to change their titles when that nation became the "Kingdom of Great Britain and Northern Ireland". Crown Prince Alexander is trying a sort of "sleight of hand" in which he retains the title "Crown Prince Alexander" but changes the "of Yugoslavia" to "of Serbia": but that then becomes a "title of pretense" rather than one he actually holds. According to his website, his claim is that he is King of Serbia, but he uses a more "modest" title. But in the real world, he gets to change the title if he becomes king, because then he will be an actual fount of honour, or when he gets an new title from the government. the choice is pretty much use his name or use his (unchanged) title. - Nunh-huh 16:13, 5 Jun 2004 (UTC)

Serbia and Yugoslavia
according to his webiste he is Prestolonaslednik Srbije i Jugoslavije I moved article to that name. Avala 13:13, 6 Jun 2004 (UTC)

Never reigned, page title wrong
The page Naming conventions (names and titles) explicitely says "do not apply an ordinal in an article title to a pretender, i.e., someone who has not reigned". We can probably mention the position of prestolonaslednik right at the start of the page but AFAICT he never reigned over anything so the title of the article needs to be fixed. --Shallot 16:50, 27 Jun 2004 (UTC)

To be explicit, the "II" part in the name needs to go. --Shallot 16:54, 27 Jun 2004 (UTC)


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Cupola (geometry)

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles are equilateral and the rectangles are squares, while the base and its opposite face are regular polygons, the triangular, square, and pentagonal cupolae all count among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively.

A cupola can be seen as a prism where one of the polygons has been collapsed in half by merging alternate vertices.

A cupola can be given an extended Schläfli symbol $2n$ representing a regular polygon $5n$ joined by a parallel of its truncation, $3n$ or ${n} || t{n}$

Cupolae are a subclass of the prismatoids.

Its dual contains a shape that is sort of a weld between half of an $n$-sided trapezohedron and a $Cnv, [1,n], (*nn),$-sided pyramid.

Examples
The above-mentioned three polyhedra are the only non-trivial convex cupolae with regular faces: The "hexagonal cupola" is a plane figure, and the triangular prism might be considered a "cupola" of degree 2 (the cupola of a line segment and a square). However, cupolae of higher-degree polygons may be constructed with irregular triangular and rectangular faces.

Coordinates of the vertices
Cupola_40.png;}} {{legend|yellow|40 rectangles;}} {{legend|red|A top regular tetracontagon;}}

and a bottom regular octacontagon (hidden).]] The definition of the cupola does not require the base (or the side opposite the base, which can be called the top) to be a regular polygon, but it is convenient to consider the case where the cupola has its maximal symmetry, $2n$. In that case, the top is a regular $n$-gon, while the base is either a regular $Cn, [1,n]^{+}, (nn),$-gon or a ${n} || t{n},$-gon which has two different side lengths alternating and the same angles as a regular ${n}$-gon. It is convenient to fix the coordinate system so that the base lies in the $n$-plane, with the top in a plane parallel to the $n$-plane. The $n$-axis is the $n$-fold axis, and the mirror planes pass through the $xy$-axis and bisect the sides of the base. They also either bisect the sides or the angles of the top polygon, or both. (If $xy$ is even, half of the mirror planes bisect the sides of the top polygon and half bisect the angles, while if $z$ is odd, each mirror plane bisects one side and one angle of the top polygon.) The vertices of the base can be designated $n$ through $z$ while the vertices of the top polygon can be designated $n$ through $n$ With these conventions, the coordinates of the vertices can be written as: $$\begin{array}{rllcc} V_{2j-1} :& \biggl( r_b \cos\left(\frac{2\pi(j-1)}{n} + \alpha\right), & r_b \sin\left(\frac{2\pi(j-1)}{n} + \alpha\right), & 0 \biggr) \\[2pt] V_{2j} :& \biggl( r_b \cos\left(\frac{2\pi j}{n} - \alpha\right), & r_b \sin\left(\frac{2\pi j}{n} - \alpha\right), & 0 \biggr) \\[2pt] V_{2n+j} :& \biggl( r_t \cos\frac{\pi j}{n}, & r_t \sin\frac{\pi j}{n}, & h \biggr) \end{array}$$

for $t{n}$.

Since the polygons $V_1$ etc. are rectangles, this puts a constraint on the values of $V_{2n},$ The distance $$\bigl|V_1 V_2 \bigr|$$ is equal to $$\begin{align} & r_b \sqrt{ \left[\cos\left(\tfrac{2\pi}{n} - \alpha\right) - \cos \alpha\right]^2 + \left[\sin\left(\tfrac{2\pi}{n} - \alpha\right) - \sin\alpha\right]^2} \\[5pt] =\ & r_b \sqrt{ \left[\cos^2 \left(\tfrac{2\pi}{n} - \alpha\right) - 2\cos\left(\tfrac{2pi}{n} - \alpha\right)\cos\alpha + \cos^2 \alpha \right] + \left[\sin^2 \left(\tfrac{2\pi}{n} - \alpha\right) - 2\sin\left(\tfrac{2\pi}{n} - \alpha\right) \sin\alpha + \sin^2 \alpha \right] } \\[5pt] =\ & r_b \sqrt{ 2\left[1 - \cos\left(\tfrac{2\pi}{n} - \alpha\right) \cos\alpha - \sin\left(\tfrac{2\pi}{n} - \alpha\right)\sin\alpha \right]} \\[5pt] =\ & r_b \sqrt{ 2\left[1 - \cos\left(\tfrac{2\pi}{n} - 2\alpha\right)\right]} \end{align}$$

while the distance $$\bigl| V_{2n+1}V_{2n+2} \bigr|$$ is equal to $$\begin{align} & r_t \sqrt{ \left[ \cos\tfrac{\pi}{n} - 1 \right]^2 + \sin^2 \tfrac{\pi}{n} } \\[5pt] =\ & r_t \sqrt{ \left[ \cos^2\tfrac{\pi}{n} - 2\cos\tfrac{\pi}{n} + 1 \right] + \sin^2\tfrac{\pi}{n} } \\[5pt] =\ & r_t \sqrt{2 \left[1 - \cos\tfrac{\pi}{n} \right]} \end{align}$$

These are to be equal, and if this common edge is denoted by $V_{2n+1}$, $$\begin{align} r_b &= \frac{s}{ \sqrt{2\left[1 - \cos\left(\tfrac{2\pi}{n} - 2\alpha \right) \right] }} \\[4pt] r_t &= \frac{s}{ \sqrt{2\left[1 - \cos\tfrac{\pi}{n} \right] }} \end{align}$$

These values are to be inserted into the expressions for the coordinates of the vertices given earlier.

Star-cupolae
Star cupolae exist for any top base ${2n}.$ where $2n$ and $V_{3n}.$ is odd. At these limits, the cupolae collapse into plane figures. Beyond these limits, the triangles and squares can no longer span the distance between the two base polygons (it can still be made with non-equilateral isosceles triangles and non-square rectangles). If $V_1 V_ 2 V_{2n+2} V_{2n+1},$ is even, the bottom base $C_{nv}$ becomes degenerate; then we can form a cupoloid or semicupola by withdrawing this degenerate face and letting the triangles and squares connect to each other here (through single edges) rather than to the late bottom base (through its double edges). In particular, the tetrahemihexahedron may be seen as a $2n$-cupoloid.

The cupolae are all orientable, while the cupoloids are all non-orientable. For a cupoloid, if $2n$, then the triangles and squares do not cover the entire (single) base, and a small membrane is placed in this base $2n$-gon that simply covers empty space. Hence the $j = 1, 2, ..., n$- and $\{n/d\}$-cupoloids pictured above have membranes (not filled in), while the $6/5 < n/d < 6$- and $\{2n/d\}$-cupoloids pictured above do not.

The height $r_b, r_t, \alpha.$ of an $\{3/2\}$-cupola or cupoloid is given by the formula: $$h = \sqrt{1 - \frac{1}{4 \sin^{2} \left( \frac{\pi d}{n} \right)}}.$$ In particular, $n/d > 2$ at the limits $\{n/d\}$ and $\{5/2\}$, and $s$ is maximized at $\{7/2\}$ (in the digonal cupola: the triangular prism, where the triangles are upright).

In the images above, the star cupolae have been given a consistent colour scheme to aid identifying their faces: the base $\{5/4\}$-gon is red, the base $\{7/4\}$-gon is yellow, the squares are blue, and the triangles are green. The cupoloids have the base $\{n/d\}$-gon red, the squares yellow, and the triangles blue, as the base $h = 0$-gon has been withdrawn.

Hypercupolae
The hypercupolae or polyhedral cupolae are a family of convex nonuniform polychora (here four-dimensional figures), analogous to the cupolas. Each one's bases are a Platonic solid and its expansion.

title: Cupola (geometry)


text:
Rico Rodriguez (musician)

Emmanuel "Rico" Rodriguez (17 October 1934 – 4 September 2015), also known as Rico, Reco or El Reco, was a Cuban-born Jamaican ska and reggae trombonist. He recorded with producers such as Karl Pitterson, Prince Buster, and Lloyd Daley. He was known as one of the first ska musicians. Beginning in the 1960s, he worked with The Members, The Specials, Jools Holland, and Paul Young.

Career
Rodriguez was born in Havana, Cuba, and at an early age moved with his family to Jamaica. He grew up there in Kingston, and was taught to play the trombone by his slightly older schoolmate Don Drummond at the Alpha Boys School. In the 1950s, Rodriguez became a Rastafarian and was closely associated musically to the rasta drummer Count Ossie.

In 1961 Rodriguez moved to the UK, where he joined live bands such as Georgie Fame's Blue Flames and started to play in reggae bands. Rodriguez also began recording with his own band, Rico's All Stars, and later formed the group Rico and the Rudies, recording the 1969 albums Blow Your Horn and Brixton Cat. In 1976 he recorded the album Man from Wareika under a contract with Island Records. In the late 1970s, he recorded a song called Offshore Banking Business with The Members and with the arrival of the 2 Tone genre, he played with ska revival bands such as The Specials including their single "A Message to You, Rudy".

Rodriguez is mentioned in the Ian Drury and The Blockheads song "Reasons to Be Cheerful, Part 3". The song was released just months before Rico joined The Specials.

In 1982, he returned to Jamaica to retire from performing professionally; however, in 1987 he returned to tour with the Heart Beat Band, and between 1992 and 1995 he would also play with Jazz Jamaica, as well as with Linton Kwesi Johnson during this era.

In 1995 Island Records released the album Roots to the Bone, an updated version of Rodriguez's earlier work Man from Wareika. From 1996, among other engagements, he played with Jools Holland's Rhythm and Blues Orchestra and also performed at various ska festivals throughout Europe with his own band. He retired from performing with Jools Holland in 2012. He was appointed a Member of the Order of the British Empire (MBE) in the 2007 New Year Honours, for services to music. In October 2012 he was awarded the Silver Musgrave Medal by the Institute of Jamaica in recognition of his contribution to Jamaican music.

Death
On 4 September 2015, following a short illness in a London hospital, Rodriguez died aged 80. A tribute to him by Youthsayers alongside Jerry Dammers was performed at the Lambeth Country Show, 2016 to a crowd of 80,000.

Discography

 * Reco in Reggae Land (Paying Tribute to Don Drummond), Pama Records (1969)
 * Man from Wareika, Island Records (1976)
 * Wareika Dub, Ghetto Rockers (1977)
 * That Man Is Forward, 2 Tone Records (1981)
 * Jama Rico, 2 Tone Records (1982)
 * Rising in the East, Jove Music (1994)
 * Return from Wareika Hill, Alpha Enterprise (1994)
 * You Must Be Crazy (live, as Rico & His Band), Grover Records (1994)
 * Wonderful World, Quattro, (1995)
 * Get Up Your Foot, (as Rico & His Band), Grover Records, (2000)
 * Going West, (as Rico & Friends), Creole Records (2002)
 * Togetherness, (as Rico Rodriguez & Roots to the Bone Band), Subterannia Discos (2005)
 * Japa-Rico - Rico Rodriguez Meets Japan,	Sony Music (2006)
 * Wareika Vibes, Jamdown (2006)

title: Rico Rodriguez (musician)


text:
Sanhattan

Sanhattan, a portmanteau of Santiago and Manhattan, is the popular ironic sobriquet given to Santiago's upscale financial district in Chile's capital. It is located to the northeast of the metropolis, in the western end of the Las Condes commune, nestled between the Mapocho River and Américo Vespucio avenue, encompassing the El Bosque Norte and El Golf barrios. A more narrow definition places it between the intersection of Andrés Bello and Vitacura avenues down to Nueva Los Leones avenue. The central street in Sanhattan is Avenida Apoquindo.

Sanhattan is home to numerous high-end buildings, including offices, restaurants, hotels, shopping centers, and banks. The district boasts two of the tallest buildings in South America, the Titanium La Portada, a 55-story tower and 194 meters in height, and the Gran Torre Santiago, a 300-meter, 63-story tower located in the nearby Providencia commune.

History

The land—known then as "Hacienda San Luis"—was acquired in 1907 from Banco de Chile bank by Ricardo Lyon, an agriculturist and mayor of Providencia commune. In 1937, a zoning scheme for Las Condes commune was defined. Architect Eduardo Lewellyn-Jones was entrusted with the task of designing a new residential area for Santiago's aristocracy. It was not until the early 1990s that real estate agencies set their sights on the area.

Today Sanhattan is among the most expensive land in Chile, with an average cost of 200 Unidad de Fomento (about US$8,300) per square meter in 2010.

Extent
According to newspaper La Tercera, Sanhattan is bounded by Av. Presidente Riesco to the north, El Golf to the east, Av. Apoquindo and Tajamar to the south, and the Mapocho river to the west.

Transport
Parking sites are few around Sanhattan, thus many people travel by subway or microbus. Line 1 of the city subway is located nearby. Sanhattan is surrounded by the Costanera Norte Highway.

title: Sanhattan


text:
Jacob Obrecht

Jacob Obrecht (also Hobrecht; 1457/8 – late July 1505) was a Flemish composer of masses, motets and songs. He was the most famous composer of masses in Europe of the late 15th century and was only eclipsed after his death by Josquin des Prez.

Life
What little is known of Obrecht's origins and early childhood comes mostly from his motet Mille quingentis. He was the only son of Ghent city trumpeter Willem Obrecht and Lijsbette Gheeraerts. His mother died in 1460 at the age of 20, and his father in 1488 in Ghent.

Details of his early education are sparse, but he probably learned to play the trumpet, like his father, and in so doing learned counterpoint and how to improvise over a cantus firmus. He is likely to have known Antoine Busnois at the Burgundian court, and certainly knew his music, since Obrecht's earliest mass shows close stylistic parallels with the elder composer.

Scholar, composer and clergyman, Obrecht seems to have had a succession of short appointments, two of which ended in less than ideal circumstances. There is a record of his compensating for a shortfall in his accounts by donating choirbooks he had copied. Throughout the period he was held in the highest esteem both by his patrons and by his fellow composers. Tinctoris, writing in Naples, singles him out in a shortlist of contemporary master composers —all the more significant because he was only 25 when Tinctoris created his list, and on the other side of Europe. Erasmus served as one of Obrecht's choirboys around 1476.

While most of Obrecht's appointments were in Flanders in the Low Countries, he made at least two trips to Italy, once in 1487 at the invitation of Duke Ercole d'Este I of Ferrara, and again in 1504. Ercole had heard Obrecht's music, which is known to have circulated in Italy between 1484 and 1487, and said that he appreciated it above the music of all other contemporary composers; consequently he invited Obrecht to Ferrara for six months in 1487. In 1504 Obrecht returned to Ferrara, but on the death of the Duke at the beginning of the next year he became unemployed. In what capacity he stayed in Ferrara is unknown, but he died in the outbreak of plague there just before 1 August 1505.

Works
Obrecht wrote mainly sacred music—masses and motets —and he also wrote some chansons.

Combining modern and archaic elements, Obrecht's style is multi-dimensional. Perhaps more than those of the mature Josquin, the masses of Obrecht display a profound debt to the music of Johannes Ockeghem in the wide-arching melodies and long musical phrases that typify the latter's music. Obrecht's style is an example of the contrapuntal extravagance of the late 15th century. He often used a cantus firmus technique for his masses: sometimes he divided his source material up into short phrases; at other times he used retrograde versions of complete melodies or melodic fragments. He once even extracted the component notes and ordered them by note value, long to short, constructing new melodic material from the reordered sequences of notes. Clearly to Obrecht there could not be too much variety, particularly during the musically exploratory period of his early twenties. He began to break free from conformity to formes fixes, especially in his chansons. Of the formes fixes, the rondeau retained its popularity longest. However, he much preferred composing Masses, where he found greater freedom. Furthermore, his motets reveal a wide variety of moods and techniques.

In his Missa Sub tuum presidium, the number of voice parts in the five movements increases from three in the Kyrie, to four in the Gloria, and so on up to seven in the Agnus Dei. The title chant is clearly heard in the top voice throughout the work, and five additional Marian chants are found in movements other than the Kyrie and Gloria: Ave preclara maris stella (Sequence verse 7, Soprano II, Credo), Aurea virga prime matris Eve (Sequence verse 9b, Soprano II and Tenor II, Sanctus), Aurea virga prime matrix Eve (Sequence verse 3b, Soprano II and Tenor I, Agnus Dei I & II), Regina caeli (Antiphon, Soprano II and Tenor I, Agnus Dei III), and Verbum bonum et suave (Sequence verse 3b, Alto I, Agnus Dei). His late four-voice mass, Missa Maria zart (tender Maria), tentatively dated to around 1504, is based on a devotional song popular in the Tyrol, which he probably heard as he went through the region around 1503 to 1504. Requiring more than an hour to perform, it is one of the longest polyphonic settings of the Mass Ordinary ever written and is considered among his finest works.

Despite working at the same period, Obrecht and Ockeghem (Obrecht's senior by some 30 years) differ significantly in musical style. Obrecht does not share Ockeghem's fanciful treatment of the cantus firmus but chooses to quote it verbatim. Whereas the phrases in Ockeghem's music are ambiguously defined, those of Obrecht's music can easily be distinguished, though both composers favor wide-arching melodic structure. Furthermore, Obrecht splices the cantus firmus melody with the intent of audibly reorganizing the motives; Ockeghem, on the other hand, does this far less.

Obrecht's procedures contrast sharply with the works of the next generation, who favored an increasing simplicity of approach (prefigured by some works of his contemporary Josquin). Although he was renowned in his time, Obrecht appears to have had little influence on subsequent composers; most probably, he simply went out of fashion along with the other contrapuntal masters of his generation.

Recordings

 * Flemish Masters, Virginia Arts Recordings, VA-04413, performed by Zephyrus, 2004. Includes the Obrecht Missa Sub tuum presidium, as well as motets by Willaert, Clemens non-Papa, Ockeghem, Des Prez, Mouton, and Gombert.
 * Obrecht, Missa Maria zart, performed by the Tallis Scholars, directed by Peter Phillips, Gimell CDGIM 032, 1996.
 * Jacob Obrecht. Chansons, Songs, Motets, Capilla Flamenca and Piffaro, Eufoda 1361, 2005
 * "Missa Sub Tuum Praesidium", The Clerks' Group, Gaudeamus, 2003.
 * "Missa Malheur Me Bat", The Clerks' Group, Gaudeamus, 1998.
 * "Missa de Sancto Donatiano", Cappella Pratensis, Fineline, 2009.
 * "Jacob Obrecht", The Sound and the Fury, ORF, 2009.
 * "Obrecht Masses", Beauty Farm, 2019, includes Missa Fortuna Desperata and Missa Maria Zart.

title: Jacob Obrecht


text:
CVF

CVF may refer to:

 * Climate Vulnerable Forum
 * Carrier Vessel Future, the project name for the Queen Elizabeth-class aircraft carrier
 * Courchevel Airport's IATA code, France
 * Cyprus Volleyball Federation
 * Competing values framework
 * Computer Vision Foundation
 * Compressed Volume File, container file for compressed FAT volumes by Microsoft DoubleSpace/DriveSpace
 * Complex-valued function, function of a complex variable
 * Center for Vigilant Freedom, predecessor to the International Civil Liberties Alliance

title: CVF


text:
E.214

In mobile telecommunications network routing, E.214 is one of three prevailing numbering plans used for delivering mobility management related messages.

The E.164 numbering plan, which is a maximum of 15 digits and usually written with a "+" prefix, is the historic first-generation format representing the phone number. The E.212 is a second-generation number plan used in America, extended to include the subscriber's MSIN (Mobile Subscription Identification Number) within the network's customer base. The E.214, developed under European GSM (Global System for Mobile Communications) standards, is a comparable extended second-generation format used outside America and can be more or less than 15 digits.

In routing a transatlantic mobile call, numbers routed from European networks are converted from E.214 numbers into E.212 numbers at the boundary incoming toward America (this can mean the Signaling Transfer Point at the edge of the American operator's network). In the outgoing direction, from America toward the rest of the world, numbers are converted from the E.212 standard to the E.214 standard.

This process, called global title translation, is the SS7 equivalent to IP routing. E.214 numbers are routed separately from E.164 numbers since they are marked with a different Numbering Plan Indicator. However, it is possible to reuse the Global Title analysis tables used E.164 numbers everywhere except for the final destination network of the message. This saves considerable administrative work.

title: E.214


text:
Species (film)

Species is a 1995 American science fiction horror film directed by Roger Donaldson and written by Dennis Feldman. It stars Ben Kingsley, Michael Madsen, Alfred Molina, Forest Whitaker, Marg Helgenberger, and Natasha Henstridge in her film debut role. The film's plot concerns a motley crew of scientists and government agents who try to track down Sil (Henstridge), a seductive extraterrestrial-human hybrid, before she successfully mates with a human male.

The film was conceived by Feldman in 1987, and was originally pitched as a film treatment in the style of a police procedural, entitled The Message. When The Message failed to attract the studios, Feldman re-wrote it as a spec script, which ultimately led to the making of the film. The extraterrestrial aspect of Sil's character was created by H. R. Giger, who was also responsible for the beings from the Alien franchise. The effects combined practical models designed by Giger collaborator Steve Johnson and XFX, with computer-generated imagery done by Richard Edlund's Boss Film Studios. Giger felt that the film and the character were too similar to Alien, so he pushed for script changes.

Most of the principal photography was done in Los Angeles, California, where the film is set. Several scenes were filmed in Utah and at the Arecibo Observatory in Puerto Rico. Species was met with mixed reviews from critics, who felt that the film's execution did not match the ambition of its premise, but nevertheless was a box office success, partly due to the hype surrounding Henstridge's nude scenes in various tabloid newspapers and lad mags of the time, grossing US$113.3 million ($ million in dollars). It spawned a franchise, which includes one theatrical sequel (Species II), as well as two direct-to-television sequels (Species III and Species – The Awakening). Species was adapted into a novel by Yvonne Navarro and two comic book series by Dark Horse Comics, one of which was written by Feldman. The film may have also influenced the legend of the chupacabra.

Plot
During the SETI program, Earth's scientists send out transmissions, such as the Arecibo message, with information about Earth and its inhabitants in the hopes of finding life beyond Earth. After receiving transmissions from an alien source on how to create limitless fuel and an alien DNA sample with instructions on how to splice it with that of humans, the scientists assume the aliens are friendly. Inspired by the second transmission, a government team led by Xavier Fitch commissions a genetic experiment meant to create a female alien/human hybrid organism under the belief that she would have "more docile and controllable" traits. They eventually produce a girl codenamed "Sil", who initially resembles a normal human and develops into a 12-year-old in three months.

Due to her violent outbursts while she is sleeping, the scientists deem her dangerous and prepare to kill her using cyanide gas, but she breaks out of her containment cell and escapes. Fearing she will mate with human males and produce offspring that will eventually exterminate the human race, the government assembles a team consisting of anthropologist Dr. Stephen Arden, molecular biologist Dr. Laura Baker, "empath" Dan Smithson, and mercenary Preston "Press" Lennox to track and kill Sil. Using her superhuman strength and intelligence and regenerative capability to evade capture, Sil matures rapidly into her early twenties and travels to Los Angeles, where she kills several people to prevent them from alerting authorities and disguise herself.

After failing to mate with and killing Robbie, a diabetic young man, and John Carey, a man she met following a car accident, Press and Baker find Sil. She assumes her alien form and flees into a nearby forest, where she kidnaps a woman to assume her identity. Secretly returning to Carey's home to spy on Fitch, Sil reads his lips and determines he and his team plan to stake out a nightclub to find her. After being spotted by Smithson, Sil lure her pursuers into a car chase wherein she leaves the woman she kidnapped to die while crashing the car into a high-voltage transformer and jumping out at the last minute. She later cuts and dyes her hair before developing an attraction towards Press, whom she dreamed of the previous night. Meanwhile, the government team celebrate Sil's apparent death at a hotel, where Sil stealthily stalks them. Arden, upset about being alone, goes to his room to find Sil waiting for him. They soon have sex, resulting in her instantly becoming pregnant before she kills him once he realizes who she is. Sensing her presence, Smithson alerts the remaining team members. Sil transforms once more and escapes into the sewers. The team pursue, but Sil kills Fitch before giving birth. Her offspring subsequently attacks Smithson, who incinerates it with a flamethrower while Press kills Sil with a grenade launcher. As the survivors leave, they fail to notice a rat gnawing on one of Sil's severed tentacles before mutating and killing another rat.

Cast

 * Natasha Henstridge as Sil
 * Michelle Williams as Young Sil
 * Dana Hee as Alien Sil
 * Frank Welker as Alien Sil (voice)
 * Ben Kingsley as Xavier Fitch
 * Michael Madsen as Preston "Press" Lennox
 * Alfred Molina as Dr. Stephen Arden
 * Forest Whitaker as Dan Smithson
 * Marg Helgenberger as Dr. Laura Baker
 * Whip Hubley as John Carey
 * Anthony Guidera as Robbie
 * Matthew Ashford as Man In Club
 * Kurtis Burow as Baby Boy, Sil's Offspring

Influence and themes
Since Sil grows rapidly and kills humans with ease, at a certain point film character Dr. Laura Baker speculates if she was a biological weapon sent by a species who thought humans were like an intergalactic weed. Feldman declared that he wanted to explore this theme further in the script, as it discussed mankind's place in the universe and how other civilizations would perceive and relate to humanity, considering that "maybe [humans are] not a potential threat, maybe a competitor, maybe a resource". He also declared that more could be said about Sil's existentialist doubts, as she does not know her origin or purpose, and only follows her instinct to mate and perpetuate the species.

Writing for the Journal of Popular Film & Television, Susan George authored a paper that dealt with the portrayal of procreation in Species, Gattaca and Mimic. George compares the character of Fitch to "an updated Dr. Frankenstein", and explores the development of Sil's maternal aspirations, which convert the character into an "archaic mother" figure similar to the xenomorph creature in the Alien series, both of which are, she claims, portrayed negatively. George further states that a recurring theme in science fiction films is a response to "this kind of powerful female sexuality and 'alien-ness in that "the feminine monster must die as Sil does at the end of Species". Feldman himself considered that an underlying theme regarded "a female arriving and seeking to find a superior mate".

A five-year investigation into accounts of the chupacabra, a well known cryptid, revealed that the original sighting report of the creature in Puerto Rico by Madeline Tolentino may have been inspired by the character Sil. This was detailed in paranormal investigator and skeptic Benjamin Radford's book Tracking the Chupacabra. According to Virginia Fugarino of Memorial University of Newfoundland writing for the Journal of Folklore Research, Radford found a link between the original eyewitness report and the design of Sil in her alien form, and hypothesized that "[Species], which [Tolentino] did see before her sighting, influenced what she believes she saw of the chupacabra".

Writing and development
Dennis Feldman had the idea for Species in 1987, as he worked on another film about an alien invasion, Real Men. Having read an article by Arthur C. Clarke about the insurmountable odds against an extraterrestrial craft ever locating and visiting Earth, given that stellar distances are great, and faster-than-light travel is unlikely, Feldman started to think that it was "unsophisticated for any alien culture to come here in what [he]'d describe as a big tin can". Thus in turn he considered that the possibility of extraterrestrial contact was through information. Then he detailed that a message would contain instructions from across the void to build something that would talk to men. Instead of a mechanical device, Feldman imagined wetware. The visitor would adapt to Earth's environment through DNA belonging to Earth's organisms. Mankind has sent to space transmissions "giving out directions" such as the Arecibo message, which Feldman considered unwary, as they relay information to potential predators from outer space. He pointed out that "in nature, one species would not want a predator to know where it hides".

Therefrom emerged a film treatment called The Message. The original script had more of a police procedural approach, with the alien being created by a "bathtub geneticist" who had just had his project aborted by the government, and a biologist who had worked on the project getting along with a police officer to search for the creature. Eventually Feldman came to believe this concept had some credibility issues, and instead changed the protagonists to a government team. After coining the name "Sil", Feldman initially thought of forming an acronym, but in the end chose only the three-letter name after learning about the codons of the genetic code, which can be represented in groups of three letters. Sil would originally emerge from a DNA sequence manipulating human DNA, and constantly mutate as she used the human junk DNA to access "all the defenses of the entire animal kingdom that [humans] evolved through – including ones that had never developed, plus ones [Earth's scientists] don't know about that have become extinct". Among the research Feldman did for the script included going to sessions of UCLA's Center for the Study of Evolution and the Origin of Life (CSEOL), talking to SETI scientists, and visiting the Salk Institute for Biological Studies to talk with researchers working on the Human Genome Project. The Message was offered to several studios, but was passed up.

In 1993, Feldman reworked his ideas into a spec script. This was sent to producer Frank Mancuso, Jr., who had hired Feldman to adapt Sidney Kirkpatrick's A Cast of Killers. The producer got attracted to the creative possibilities as the film offered "the challenge of walking that fine line between believability and pushing something as far as it can go". Metro-Goldwyn-Mayer got interested on the project, and while Feldman had some initial disagreements on the budget, after considering other studios he signed with MGM. In turn, the now retitled Species attracted director Roger Donaldson, who was attracted to its blend of science fiction and thriller. The script underwent eight different drafts, written over an eight-month period, before Donaldson was content that flaws in the story's logic had been corrected. At one point another writer, Larry Gross, tried his hand with the script, but ultimately all the work was done by Feldman. Feldman would remain as a co-producer. While the initial Species script suggested a love triangle between Sil and two government team members, the dissatisfaction of the crew eventually led to changes to the ending, which ended up featuring Sil having a baby that would immediately prove dangerous.

When Donaldson was announced as the director in 1994, Mancuso stated that most of the $35 million budget would be spent on effects, as "it's not a movie that calls for stars. We're going to try and put as much money as we can below the line and allow the effects and the creature to be the highlights of the film". The lesser emphasis on actors included a newcomer, former model Natasha Henstridge, as the human version of the creature Sil.

Design
Sil was designed by Swiss artist H. R. Giger, who also created the creatures in the Alien films. Donaldson thought Giger was the best man for the film after reading his compendium Necronomicon, and eventually he and Mancuso flew to Switzerland to meet the artist. What attracted Giger was the opportunity to design "a monster in another way—an aesthetic warrior, also sensual and deadly, like the women look in [his] paintings". While Giger opted to stay in Switzerland to take care of his dying mother instead of flying to Los Angeles to accompany production, he built some puppets in his own studio, and later faxed sketches and airbrush paintings as production went through.

The practical models were made by Steve Johnson and his company XFX, which had already worked with Giger's designs in Poltergeist II: The Other Side. Giger had envisioned more stages of Sil's transformation, but the film only employed the last one, where she is "transparent outside and black inside—like a glass body but with carbon inside", with XFX doing the translucent skin based on what they had done for the aliens of The Abyss. Sil's alien form had both full-body animatronics with replaceable arms, heads and torsos, and a body suit. Richard Edlund's Boss Film Studios was hired for over 50 shots of computer-generated imagery, which included one of the earliest forms of motion capture effects. Using a two-foot-high (60 cm) electric puppet that had sensors translating its movements to a digital Sil, Boss Films managed to achieve in one day what would have once taken as much as three weeks with practical effects.

Giger was unhappy with some elements he found to bear similarity with other films, particularly the Alien franchise. At one point he sent a fax to Mancuso finding five similarities: a "chestburster" (as Sil giving birth echoed the infant Alien breaking out of its host's chest), the creature having a punching tongue (Giger at first wanted Sil's tongue to be composed of barbed hooks), a cocoon, the use of flame throwers, and having Giger as the creature designer. A great point of contention was the ending, which Giger considered derivative from the climaxes from both Alien 3 and Terminator 2: Judgment Day. The designer felt that horror films frequently held some final confrontation with fire, which he considered old-fashioned and linked to medieval witch trials. He sent some ideas for the climax to the producers, with them accepting to have Sil's ultimate death occurring by headshot.

Filming
Filming happened mostly in Los Angeles, including location shooting at Sunset Strip, Silver Lake, Pacific Palisades, the Hollywood Hills and the Biltmore Hotel. Id Club, the nightclub featured in the film, was built within Hollywood's Pantages Theater, while the hills above Dodger Stadium near Elysian Park were used for the car chase and crash where Sil fakes her death. For the opening scenes in Utah, the Tooele Army Depot dubbed as the outside of the research facility—the interiors were shot at the Rockwell International Corporation laboratory in California—and a Victorian-era train station in Brigham City was part of Sil's escape. Other locations included the Santa Monica Pier and the Arecibo Telescope in Puerto Rico. The most complex sets involved the sewer complex and a tar-filled granite cavern where the ending occurs. Donaldson wanted a maze quality for the sewers, which had traces of realism (such as tree roots breaking through from the ceiling) and artistic licenses. Production designer John Muto intentionally designed the sewers wider and taller than real ones, as well as with walkways, but nevertheless aiming for a claustrophobic and realistic atmosphere. The tunnels were built out of structural steel, metal rod, plaster and concrete to endure the fire effects, and had its design based on the La Brea Tar Pits, with Muto describing them as "just the sort of place in which a creature from another planet might feel at home".

Release
Species received a wide theatrical release on July 7, 1995. Its opening weekend was $17.1 million, MGM's biggest opening at the time and ranked second in the box office ranking behind Apollo 13. Budgeted at $35 million, the film earned a total of $113 million worldwide ($ million adjusted for inflation), including $60 million in the United States. Audiences polled by CinemaScore during opening weekend gave the film an average grade of "B−" on a scale ranging from A+ to F.

MGM Home Entertainment released the film on DVD in March 1997, which contains a booklet with trivia and production notes, and on VHS in August 1999. In July 2006, Sony Pictures Home Entertainment released it on Blu-ray, whose supplements includes several featurettes as well as two audio commentary tracks: one by director Roger Donaldson, Natasha Henstridge and Michael Madsen, and another from Donaldson, cinematographer Andrzej Bartkowiak, make-up effects creator Steve Johnson, visual effects supervisor Richard Edlund and producer Frank Mancuso Jr. In July 2017, Scream Factory released a collector's edition Blu-ray, issued with a concoction of new and archival bonus contents which have been ported over from original DVD and Blu-ray versions.

Reception
On review aggregator Rotten Tomatoes, the film received an approval rating of 42% based on 73 reviews, with an average rating of 5.30/10 and a critical consensus which reads: "Species shows flashes of the potential to blend exploitation and sci-fi horror in ingenious ways, but is ultimately mainly interested in flashing star Natasha Henstridge's skin". On Metacritic, the film has a weighted average score of 49 out of 100 based on 25 critics, indicating "mixed or average reviews".

Roger Ebert gave it 2 out of 4 stars, criticizing the film's plot and overall lack of intelligence. Cristine James from Boxoffice magazine gave the film 2 out of 5 stars, describing it as "Alien meets V meets Splash meets Playboy's Erotic Fantasies: Forbidden Liaisons, diluted into a diffuse, misdirected bore". James Berardinelli gave the film 2½ out of 4 stars, stating that "as long as you don't stop to think about what's going on, Species is capable of offering its share of cheap thrills, with a laugh or two thrown in as well". Owen Gleiberman of Entertainment Weekly found the film lacking in imagination and special effects, also commenting that Alfred Molina "sport[s] a haircut that's scarier than the creature". Variety's review of the film described it as a "gripping if not overly original account of an extraterrestrial species attempting to overwhelm our own" and that Ben Kingsley and other lead actors "have only two-dimensional roles to engage them". The review notes the similarity between H.R. Giger's design of Sil and his work on Alien.

Scott Weinberg of DVD Talk praised the acting, Feldman's screenplay and Donaldson's direction. He concluded by saying that Species makes for "a very good time for the genre fans". Mick LaSalle, writing for San Francisco Chronicle, was notedly less enthusiastic, quipping that if "Species were a little bit worse, it would have a shot at becoming a camp classic". Los Angeles Times critic Peter Rainer described Species as "a pretty good Boo! movie", finding it an entertaining thriller while unoriginal and with ineffective tonal shifts.

Adaptations
Yvonne Navarro co-wrote a novelization based on the original screenplay with Dennis Feldman. The book gives several in-depth details about the characters not seen in the film, such as Sil's ability to visualize odors and determine harmful substances from edible items by the color. Gas appears black, food appears pink, and an unhealthy potential mate appears to give off green fumes. Other character details include Preston's background in tracking down AWOL soldiers as well as the process of decoding the alien signal. Although no clues are given as to its origin, it is mentioned that the message was somehow routed through several black holes to mask its point of origin. An audiobook version narrated by Alfred Molina won the Audie Award for Solo Performance.

Dark Horse Comics published a four-issue comic book adapting the film, written by Feldman and penciled by Jon Foster. Dark Horse would also publish a mini-series with an all-new storyline, Species: Human Race, released in 1997. West End Games released a World of Species sourcebook for its Masterbook role-playing game system. MGM had partnered with Cyberdreams to make a computer game based on the film, and while the company managed to release an H.R. Giger screen saver featuring Species images, the game never came to be due to Cyberdreams' closure.

Sequels
The first sequel to Species, Species II was released theatrically on April 10, 1998. The film depicts astronauts on a mission to Mars being attacked by the aliens from Species, and the events that ensue upon their return to Earth. There, Dr. Baker has been working on Eve, a more docile clone of Sil. Madsen and Helgenberger reprised their roles, while Henstridge played Eve. Species II received overwhelmingly negative reviews from critics, garnering a 9% approval rating at Rotten Tomatoes, and Madsen denounced it as a terrible film. The film's director, Peter Medak, attributed the failure of the film to not picking up the infected rat ending of the original film. Navarro later authored the novelization for Species II which followed the film's original screenplay with added scenes.

The second sequel, Species III, followed in 2004. It premiered on Sci-Fi Channel on November 27, with a DVD release on December 7. The film's plot starts where Species II ends, revolving around Sunny Mabrey's character Sara, the daughter of Eve, reared by a doctor played by Robert Knepper. Sara, an alien-human hybrid, seeks other hybrids to mate with. Henstridge appears in a cameo at the beginning of the film. Two out of six critics mentioned on Rotten Tomatoes gave it a positive rating, with DVD Talk's reviewer noting that it is "a more cohesive and sensible flick than [Species II] is, but ultimately, it's just a lot of the same old schtick", while Film Freak Central called it "amateurish" and "vapid". A fourth film, Species: The Awakening came out in 2007, following the schedule of Species III of Sci-Fi Channel premiere and subsequent DVD release. None of the actors from the original film returned in this sequel, which instead starred Helena Mattsson as the alien-hybrid seductress.

title: Species (film)


text:
Onuf's nucleus

Onuf's nucleus is a distinct group of neurons located in the ventral part (lamina IX) of the anterior horn of the sacral region of the human spinal cord involved in the maintenance of micturition and defecatory continence, as well as muscular contraction during orgasm. It contains motor neurons, and is the origin of the pudendal nerve. The sacral region of the spinal cord is the fourth segment (cervical, thoracic, and lumbar being the first three) of vertebrae in the spinal cord which consists of the vertebrae 26-30. While working in New York City in 1899, Bronislaw Onuf-Onufrowicz discovered this group of unique cells and originally identified it as “Group X.” “Group X” was considered distinct by Onufrowicz because the cells were different in size from the surrounding neurons in the anterolateral group, suggesting that they were independent.

Structure
Onuf's nucleus is a distinct group of neurons located in the ventral part (lamina IX) of the anterior horn of the sacral region of the human spinal cord involved in the maintenance of micturition and defecatory continence, as well as muscular contraction during orgasm. It contains motor neurons, and is the origin of the pudendal nerve. The sacral region of the spinal cord is the fourth segment (cervical, thoracic, and lumbar being the first three) of vertebrae in the spinal cord which consists of the vertebrae 26-30.

This small group of neural cells is located between S1 and S2 or S2 and S3 and although Onuf's nucleus is located primarily in S2, it can extend to the caudal end of the first sacral segment or to the middle part of the third sacral segment. Also, Onuf's nucleus is found almost symmetrically on both sides of the ventral horn. This innervation, or nerve supply, is arranged in a neuropil and averages approximately 625 neurons in both the left and right ventral horns, and measures about 4–6 mm on each side. In other animals it averages approximately 300-500 on both sides.

Many staining techniques have been used to study the anatomy of Onuf's nucleus. The Nissl method was commonly used as well as myelin sheath stains and silver stains. Use of the Klüver-Barrera staining method showed that Onuf's nucleus appears clear due to the presence of many vertically arranged unmyelinated fibers. The sizes of the cells in Onuf's nucleus are small in comparison to other lateral group cells. The neurons in Onuf's nucleus are motoneurons, and like most motoneurons they are characterized by their multipolarity and large Nissl bodies.

Function
Onuf's nucleus is the origin of innervation for the striated muscles of the rectum and urethral sphincters. The neurons of Onuf's nucleus are responsible for controlling external sphincter muscles of the anus and urethra in humans. Onufrowicz also proposed that Onuf's nucleus controlled the ischiocavernosus and bulbocavernosus muscles which function in penile erection and ejaculation in males. The dorsomedial subnucleus innervates the external anal sphincter and the ventrolateral subgroup connects to the external urethral sphincter.

Somatic

 * The motor neurons of Onuf's nucleus innervate striated musculature (rhabdosphincter muscle) which is controlled voluntarily.
 * Neurons in Onuf's nucleus lack autonomic dense-core vesicles even though they receive the same synaptic endings as alpha motor neurons.
 * A study by Bergmann et al. showed that Onuf nucleus cells have the same cytoskeletal abnormalities as alpha motor neurons in motor neuron disease/amyotrophic lateral sclerosis.

Autonomic

 * Diseases characterized by disturbances in urination and defecation affect autonomic and Onuf's nucleus cells similarly.
 * Both cell types are spared by amyotrophic lateral sclerosis.
 * Onuf's nucleus cells are anatomically linked with the sacral parasympathetic motor neurons and have many peptidergic nerve terminals.
 * Cells in Onuf's nucleus resemble autonomic neurons and do not receive afferents from adjacent neurons.

Neurotransmitters in Onuf's nucleus
The motoneurons in Onuf's nucleus contain a dense array of serotonin and norepinephrine receptors and neurotransmitters and are activated by glutamate. When the 5-HT and NE receptors are stimulated, the guarding reflex occurs to prevent voiding of the bladder caused by unexpected abdominal pressure.

Sexual dimorphism
Onuf's nucleus is sexually dimorphic, meaning that there are differences in Onuf's nucleus between males and females of the same species. Sexual dimorphism of Onuf's nucleus has been found in dogs, monkeys, and humans. Males of these species have more of these motoneurons than do their female counterparts. It has also been shown that the sex differences in Onuf's nucleus can be reduced (or in some cases eliminated) by exposing a prenatal female to high levels of androgen.

Urinary stress incontinence
Stress urinary incontinence (SUI) is a common disease in women caused by pelvic floor muscle weakness. Coughing, laughing, sneezing, exercising or other movements that increase intra-abdominal pressure, and thus increase pressure on the bladder, are common reasons for urine loss.

There are three layers of muscle that are known to control urine flow through the urethra; an inner band of longitudinal smooth muscle, a middle band of circular smooth muscle, and an external band of striated muscle called the rhabdosphincter. The urethra is controlled by the sympathetic, parasympathetic, and somatic divisions of the peripheral nervous system. The sympathetic innervation (nerve supply) comes from the sympathetic preganglionic neurons located in the upper lumbar spinal cord along the hypogastric nerve and terminates in the longitudinal and circular smooth muscle layers in the urethra. The parasympathetic nerve supply comes from the parasympathetic preganglionic neurons in the sacral spinal cord and also terminates in the longitudinal and circular smooth muscle layers. Finally the somatic nerve supply arises from the urethral sphincter motor neurons in the ventral horn of the sacral spinal cord; better known as Onuf's nucleus. The pudendal nerve that extends from Onuf's nucleus, connects directly to the rhabdosphincter muscle to control micturation.

The sympathetic storage reflex or pelvic-to-hypo-gastric reflex is initiated when the bladder swells. Stretch receptors cause postganglionic neurons to release norepinephrine (NE). NE causes the bladder to relax and the urethra to contract, thus preventing urine loss. The somatic storage reflex or the pelvic-to-pudendal or guarding reflex is initiated when one laughs, sneezes, or coughs, which causes increased bladder pressure. Glutamate is the primary excitatory transmitter for the reflex. Glutamate activates NMDA and AMPA receptors which produce action potentials. These action potentials activate the release of acetylcholine causing the rhabdosphincter muscle fibers to contract. When the guarding reflex does not function normally, SUI occurs.

 * Duloxetine

Onuf's nucleus controls rhabdosphincter motor neurons and has been shown to contain a dense array of 5-HT (serotonin) and NE terminals. 5-HT and NE were shown to inhibit bladder activity. In 2005, researchers Wolfgang H. Jost and Parvaneh Marsalek used serotonin norepinephrine reuptake inhibitors (SNRI) to increase the synaptic levels of both 5-HT and NE in the synaptic cleft. Duloxetine hydrochloride, a SNRI, has been shown to increase bladder capacity and sphincteric muscle activity in animals and humans exhibiting irritated bladder function. Duloxetine is the first medication developed to help SUI. This is promising because Duloxetine also showed no effect on bladder contraction force or duration which suggests that Duloxetine is affecting the sensory limb of the urination process. 5-HT and NE do not function through direct excitation of motor neurons but facilitate the effects of glutamate. When glutamatergic activation in sphincter motor neurons is absent there is no effect of NE or 5-HT (seen during micturition contraction).

Amyotrophic lateral sclerosis
Amyotrophic lateral sclerosis ( Lou Gehrig disease ) is a disease that causes degeneration of motoneurons that control voluntary muscle movement. Surprisingly, the bladder and rectum sphincters remain normal even during the final terminal stages of the illness. Since these muscles are controlled by Onuf's nucleus, it is of great importance in the study of this disease. In amyotrophic lateral sclerosis, Onuf's nucleus is preserved but the other anterior horn cell groups atrophy. This discovery reinforced the notion that Onuf's nucleus controlled the muscles related to sphincter function in the anus and urethra.

In a study conducted by Kihira et al., eight individuals with amyotrophic lateral sclerosis were compared to nine control cases. The results indicated that the total number of neurons in Onuf's nucleus in patients with amyotrophic lateral sclerosis did not differ from the control patients. However, normal neurons decreased in number while atrophic neurons increased. It was also shown that the decrease in the number of normal neurons was not due to aging. Patients with amyotrophic lateral sclerosis also contain less RNA in their motoneurons than normal individuals. The decrease in RNA is correlated with the decrease in size of the nucleolus. Thus, the size of the nucleolus may be an early indicator of amyotrophic lateral sclerosis.

There is often sparing of Onuf's nucleus in spinal muscular atrophy type 1.

Shy–Drager syndrome
In order to study Onuf's nucleus from the opposite perspective (meaning cases where it was not preserved) studies were done on Shy–Drager syndrome. Shy–Drager syndrome is a rare neurodegenerative disease that attacks the autonomic nervous system. Since the main symptom of Shy–Drager syndrome is incontinence it makes it a good candidate to study its effects on Onuf's nucleus. When the sacral sections of the spinal cord were studied in patients with Shy–Drager syndrome, it was revealed that cell death was confined to the area of Onuf's nucleus. This, once again, verified the role Onuf's nucleus in vesicorectal function.

History
While working in New York City in 1899, Bronislaw Onuf-Onufrowicz discovered this group of unique cells and originally identified it as “Group X.” “Group X” was considered distinct by Onufrowicz because the cells were different in size from the surrounding neurons in the anterolateral group, suggesting that they were independent.

Other animals
Onuf's nucleus is not specific only to humans. As mentioned before, the motor neurons of the external urethral sphincter and the external anal sphincter are found in ventral horn of the second sacral segment known as Onuf's nucleus. Using horseradish peroxidase to stain the neurons, it has been determined that the external anal sphincter motoneurons are located in dorsomedial to the external urethral sphincter motoneuron in the cat, dog, monkey, golden hamster, as well as the man. However, the location of these motoneurons differs in the rat, Mongolian gerbil and domestic pig. In the rat, these motoneurons are located in separate cell groups.

In addition to differences among location of the motoneurons responsible or sphincter function, it is important to mention the differences in sexual dimorphism between species. Although sexual dimorphism of Onuf's nucleus is present in all species, the extent of the sexual dimorphism varies. For example, sexual dimorphism in the number of perineal motoneurons is less obvious in dogs and humans than it is in rats. This is to be expected because female dogs retain perineal muscles whereas female rats do not have perineal muscles. As in humans, prenatal androgen plays an important role in establishing the sex differences in Onuf's nucleus of these species. If a female is exposed to excess androgen during the prenatal period, the sexual dimorphism does not occur in Onuf's nucleus.

title: Onuf's nucleus


text:
Sainte-Foy

Sainte Foy or Sainte Foi (French, 'Saint Faith' or 'holy faith') may refer to:

France

 * Sainte-Foi, in the Ariège département
 * Sainte-Foy, Landes, in the Landes département
 * Sainte-Foy, Saône-et-Loire, in the Saône-et-Loire département
 * Sainte-Foy, Seine-Maritime, in the Seine-Maritime département
 * Sainte-Foy, Vendée, in the Vendée département
 * Sainte-Foy-d'Aigrefeuille, in the Haute-Garonne département
 * Sainte-Foy-de-Belvès, in the Dordogne département
 * Sainte-Foy-de-Longas, in the Dordogne département
 * Sainte-Foy-de-Montgommery, in the Calvados département
 * Sainte-Foy-de-Peyrolières, in the Haute-Garonne département
 * Sainte-Foy-la-Grande, in the Gironde département
 * Sainte-Foy-la-Longue, in the Gironde département
 * Sainte-Foy-l'Argentière, in the Rhône département
 * Sainte-Foy-lès-Lyon, in the Rhône département
 * Sainte-Foy-Saint-Sulpice, in the Loire département
 * Sainte-Foy-Tarentaise, in the Savoie département
 * Abbey Church of Sainte-Foy, in Conques, Aveyron département

North America

 * Sainte-Foy, Quebec City, Canada
 * Sainte-Foy station

People

 * Charles-Louis Sainte-Foy (1817–1877), French opera singer
 * Saint Faith, 3rd-century French saint, Sainte-Foy in French

title: Sainte-Foy


text:
Spherical pendulum

In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass $m$ moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.

Owing to the spherical geometry of the problem, spherical coordinates are used to describe the position of the mass in terms of $(r, \theta, \phi)$, where $r$ is fixed such that $$r = l$$.

Lagrangian mechanics
Routinely, in order to write down the kinetic $$T=\tfrac{1}{2}mv^2$$ and potential $$V$$ parts of the Lagrangian $$L=T-V$$ in arbitrary generalized coordinates the position of the mass is expressed along Cartesian axes. Here, following the conventions shown in the diagram,
 * $$x=l\sin\theta\cos\phi$$
 * $$y=l\sin\theta\sin\phi$$
 * $$z=l(1-\cos\theta)$$.

Next, time derivatives of these coordinates are taken, to obtain velocities along the axes
 * $$\dot x=l\cos\theta\cos\phi\,\dot\theta-l\sin\theta\sin\phi\,\dot\phi$$
 * $$\dot y=l\cos\theta\sin\phi\,\dot\theta+l\sin\theta\cos\phi\,\dot\phi$$
 * $$\dot z=l\sin\theta\,\dot\theta$$.

Thus,

v^2=\dot x ^2+\dot y ^2+\dot z ^2 =l^2\left(\dot\theta ^2+\sin^2\theta\,\dot\phi ^2\right) $$

and

T=\tfrac{1}{2}mv^2 =\tfrac{1}{2}ml^2\left(\dot\theta ^2+\sin^2\theta\,\dot\phi ^2\right) $$

V=mg\,z=mg\,l(1-\cos\theta) $$

The Lagrangian, with constant parts removed, is

L=\frac{1}{2} ml^2\left( \dot{\theta}^2+\sin^2\theta\ \dot{\phi}^2 \right) + mgl\cos\theta. $$

The Euler–Lagrange equation involving the polar angle $$\theta$$

\frac{d}{dt}\frac{\partial}{\partial\dot\theta}L-\frac{\partial}{\partial\theta}L=0 $$ gives

\frac{d}{dt} \left(ml^2\dot{\theta} \right) -ml^2\sin\theta\cdot\cos\theta\,\dot{\phi}^2+ mgl\sin\theta =0 $$ and

\ddot\theta=\sin\theta\cos\theta\dot\phi ^2-\frac{g}{l}\sin\theta $$ When $$\dot\phi=0$$ the equation reduces to the differential equation for the motion of a simple gravity pendulum.

Similarly, the Euler–Lagrange equation involving the azimuth $$\phi$$,

\frac{d}{dt}\frac{\partial}{\partial\dot\phi}L-\frac{\partial}{\partial\phi}L=0 $$ gives

\frac{d}{dt} \left( ml^2\sin^2\theta  \cdot   \dot{\phi} \right) =0 $$. The last equation shows that angular momentum around the vertical axis, $$|\mathbf L_z| = l\sin\theta \times ml\sin\theta\,\dot\phi$$ is conserved. The factor $$ml^2\sin^2\theta$$ will play a role in the Hamiltonian formulation below.

The second order differential equation determining the evolution of $$\phi$$ is thus
 * $$\ddot\phi\,\sin\theta = -2\,\dot\theta\,\dot{\phi}\,\cos\theta$$.

The azimuth $$\phi$$, being absent from the Lagrangian, is a cyclic coordinate, which implies that its conjugate momentum is a constant of motion.

The conical pendulum refers to the special solutions where $$\dot\theta=0$$ and $$\dot\phi$$ is a constant not depending on time.

Hamiltonian mechanics
The Hamiltonian is

 * $$H=P_\theta\dot \theta + P_\phi\dot \phi-L$$

where conjugate momenta are

 * $$P_\theta=\frac{\partial L}{\partial \dot \theta}=ml^2\cdot \dot \theta$$

and

 * $$P_\phi=\frac{\partial L}{\partial \dot \phi} = ml^2 \sin^2\! \theta \cdot \dot \phi$$.

In terms of coordinates and momenta it reads

$$H = \underbrace{\left[\frac{1}{2}ml^2\dot\theta^2 + \frac{1}{2}ml^2\sin^2\theta\dot \phi^2\right]}_{T} + \underbrace{ \bigg[-mgl\cos\theta\bigg]}_{V}= {P_\theta^2\over 2ml^2}+{P_\phi^2\over 2ml^2\sin^2\theta}-mgl\cos\theta$$

Hamilton's equations will give time evolution of coordinates and momenta in four first-order differential equations

 * $$\dot {\theta}={P_\theta \over ml^2}$$
 * $$\dot {\phi}={P_\phi \over ml^2\sin^2\theta}$$
 * $$\dot {P_\theta}={P_\phi^2\over ml^2\sin^3\theta}\cos\theta-mgl\sin\theta$$
 * $$\dot {P_\phi}=0$$

Momentum $$P_\phi$$ is a constant of motion. That is a consequence of the rotational symmetry of the system around the vertical axis.

Trajectory
Trajectory of the mass on the sphere can be obtained from the expression for the total energy

 * $$E=\underbrace{\left[\frac{1}{2}ml^2\dot\theta^2 + \frac{1}{2}ml^2\sin^2\theta \dot \phi^2\right]}_{T}+\underbrace{ \bigg[-mgl\cos\theta\bigg]}_{V}$$

by noting that the horizontal component of angular momentum $$L_z = ml^2\sin^2\!\theta \,\dot\phi$$ is a constant of motion, independent of time. This is true because neither gravity nor the reaction from the sphere act in directions that would affect this component of angular momentum.

Hence

 * $$E=\frac{1}{2}ml^2\dot\theta^2 + \frac{1}{2}\frac{L_z^2}{ml^2\sin^2\theta}-mgl\cos\theta$$
 * $$\left(\frac{d\theta}{dt}\right)^2=\frac{2}{ml^2}\left[E-\frac{1}{2}\frac{L_z^2}{ml^2\sin^2\theta}+mgl\cos\theta\right]$$

which leads to an elliptic integral of the first kind for $$\theta$$

 * $$t(\theta)=\sqrt{\tfrac{1}{2}ml^2}\int\left[E-\frac{1}{2}\frac{L_z^2}{ml^2\sin^2\theta}+mgl\cos\theta\right]^{-\frac{1}{2}}\,d\theta$$

and an elliptic integral of the third kind for $$\phi$$

 * $$\phi(\theta)=\frac{L_z}{l\sqrt{2m}}\int\sin^{-2}\theta \left[E-\frac{1}{2}\frac{L_z^2}{ml^2\sin^2\theta}+mgl\cos\theta\right]^{-\frac{1}{2}}\,d\theta$$.

The angle $$\theta$$ lies between two circles of latitude, where

 * $$E>\frac{1}{2}\frac{L_z^2}{ml^2\sin^2\theta}-mgl\cos\theta$$.

title: Spherical pendulum


text: User:Dtewfik

title: User:Dtewfik


text:
Saint-Germain-la-Blanche-Herbe

Saint-Germain-la-Blanche-Herbe is a commune in the Calvados department in the Normandy region in northwestern France.

title: Saint-Germain-la-Blanche-Herbe