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Earth Stewardship/Blackbelt

Environmental Awareness
* Survivalistic Vision - Archaic-instinctive—survivalistic/automatic/reflexological

Purpose - Curiosity

 * Precept 1: Adopt a ’set to break sets’: Think different, get people that think different, take different perspective, different different different

 * Precept 2: Explore the ‘givens’: Context is important for a problem. Maybe the context was wrong. Use Assumption surfacing or Reversals to get behind it. Get a fresh view on it. Try being very clear about your environment, trying to notice things you take for granted.

 * Precept 3: Broad picture, local detail: You can store an enormous amount of information, but only very few items at a time. Use mind maps or similar techniques to go broad and deep at the same time or rather one after the other.

Spiral Dynamics - Beige CODE,

Instructor : Rhys Thomas

Center of activity : red

Survival (as an individual and as a planet), our need for world peace and environmental balance.

Element:Earth

Area of conciousness : physical body, and requires you to be physically present within the ESA.

Key Words: stability, solidarity, unity and form.

* Learning outcome 1 - To understand the Principles of Gender

Objective 1 Develop your online profile

Objective 2 "Express self to meet imperative physiological needs through instincts of Homo sapiens."

Objective 3 Prioritise improvement activities for greatest positive environmental impacts.

Action 1 Enrol on the Eco Ambassador programme by clicking on this link.

Action 2 Read about the programme and join the ESAI support group.

Action 3 Join the ESAI forum.

Evidence for Action 1

Evidence for action 2

Evidence for action 3

Earth Stewardship
* Tribal Vision - Animistic-tribalistic magical-animistic Tribal order

Purpose - Forgiveness

 * Precept 4: Value play: Play is central to learning, just think about being a kid. You learn by trial and error. It loosens things up if you can just play with a problem. For this you need to create a special settings, choose team members that trust each other and you can simply use such techniques as a way to build a team.

 * Precept 5: Build up, don’t knock down: Go from ‘Yes, but…’ to ‘Yes, and…’. Value people.

 * Precept 6: Live with Looseness: Things will be confusing, uncertain, contradictory, sceptical and more. Especially in whicked problems you need to live with it and let go to have a map built over time.

Spiral Dynamics - Purple

Instructor : Penny Rose

Center of activity : orange

Element: Water (Where attention flows, energy goes)

Area of conciousness: emotional

Moving beyond understanding of ourselves and realising the awareness of others-desires.

Key Words: difference, seperation, change, duality, and movement

* Learning outcome 1 - To understand the Principles of Vibration

Objective 1 "Sacrifice to the ways of the elders and customs as one subsumed in group."

Objective 2 Establish your group identity as a community of enquiry.

Objective 3 Define improvement projects which satisfy group requirements.

Action 1 Update bios so we know who you are, and what you can do, and why you want to do it.

Action 2 Enter group collaborative excercises by joining the PALTALK community of practice.

Action 3 Begin your training as an Eco-Ambassador.

Evidence for Action 1

Evidence for action 2

Evidence for action 3

Becoming part of an Alliance
*  Vision - RED Egocentric-exploitive power gods/dominionist

Spiral Dynamics - Red

Purpose - Love (Human Emmergence)

 * Precept 7: It is there already - nurture it: Creativity is probably already there, well below its potential. Try removing soem barriers. Delegate, make ideas welcome, schedule idea time.

 * Precept 8: Involve others: We all have different view, and something normal for us might not be for somebody else. New ideas come from this. Enjoy the differences.

 * Precept 9: Connect and be receptive: ideas can be triggered from your environment. These can be related to the problem or not. You need to link problems and triggers.

Instructors : Deborah Heaton-King / Gaynor Linnocor

Center of activity : yellow

Element: Fire

Area of consciousness: intellectual body that includes thoughts, opinions, and judgments.

Key Words: Industry, energy, action, power, and will

* Learning outcome 1 - To understand the Principles of Polarity

Objective 1 Join an environmental campaign that interests you

Objective 2 Generate a power point presentaiton or similar and communicate with group members

Objective 3 Write up an LSOE in a format that suits, Pictures, Notes, Information, emails etc

Action 1

Action 2

Action 3

Evidence for Action 1

Evidence for action 2

Evidence for action 3

Earth Stewardship Alliance Admin
* Vision - Purposeful / authoritarian Vision -

Purpose - Sense of Direction

 * Precept 10: Know what you really want: As they say “if you don’t know where you want to go, you probably won’t get there”. The way is not important, or rather needs to be loose, but the goal should be clear.

Spiral Dynamics - Blue

Instructor : Dr Peter James

Color: Green

Element: Air

Environmental Area of focus :

Key words : Balance

* Learning outcome 1 - To understand the Principles of Cause and effect

Objective 1 Learn about Globcal and the Model International Court for the Environment

Objective 2 Collaborate and generate ideas after viewing group presentations

Objective 3 Develop a position paper

Action 1 Collaborate using the PALTALK system

Action 2 Liase between groups and collect data

Action 3 Understand codes of practice and code of conduct

Evidence for Action 1

Evidence for action 2

Evidence for action 3

Earth Stewardship Alliance Officer
* Vision - Scientific or Strategic - Multiplistic-achievist

Purpose - Sense of Direction

 * Precept 11: Cycle often and close late: Try not to appear decisive, or stop at the first solution. Cycle a few times to allow extra deeper information to filter in.

 * Precept 12: Manage the process: People, Place and Process. These are important and should be managed.

Spiral dynamics - Orange

Instructor - Liase with other group officers with help from Lois Loyd and Deborah Heaton-King

Color: blue (Situated: in the realm of communication)

Element: Sound

Area of environmental consciousness: through suitable media

Key Words: sound, vibration, communication, and self-expression

* Learning outcome 1 - To understand the Principles of Corrspondance

Objective 1 Complete ESA surveys

Objective 2 Analyse and communicate data and try to uncover or understand route causes.

Objective 3 Collaborate with others and uncover resource requirements.

Action 1 Networking

Action 2 Set up a corrective actions requirements.

Action 3 Delegate communication responsibilities and keep records.

Evidence for Action 1

Evidence for action 2

Evidence for action 3

ESA International (International Admins and officers)
* Vision - Relativistic Communitarian - Relativistic-personalistic—communitarian/egalitarian

Instructor - Lois Loyd

Color: Indigo

Element: Light

Area of consciousness: International

It is here that we have "sixth sight," or the ability to "see" by way of receiving insight or inspiration from the global mind.

Key Words: intuition, imagination, creative problem solving.

* Learning outcome 1 - To understand the Principles of Rhythm

Objective 1 "Sacrifice self interest now in order to gain acceptance and group harmony."

Objective 2 Improve the selected process in order to reduce variability.

Objective 3 Understand risks.

Action 1 Look at situational issues, obstacles and conflicts.

Action 2 Implementation of actions register.

Action 3 Risk reduction and removal of re-occurances.

Evidence for Action 1

Evidence for action 2

Evidence for action 3

Eco Ambassador
* Vision - Systemic-integrative

Instructor : Jay Wooldridge

Spiral Dunamics : Yellow

Color : white (some believe violet)

Element : Thought

Center of activity : www.esa-international.eu (Forums)

Key Words: International Knowing and Global Consciousness

* Learning outcome 1 - To understand the Principles of Enviro-Mentalism

Objective 1

Objective 2

Objective 3

Action 1

Action 2

Action 3 Set up control to prevent re-occurances and consolidate gains.

Evidence for Action 1

Evidence for action 2

Evidence for action 3

title: Earth Stewardship/Blackbelt


text:
Portal:Thai

Thai has 44 consonant letters and 15 vowel letters. Thai has tones so please use it carefully. For more information about the Thai alphabet.

 * ก K
 * ข KH
 * ค KH
 * ฆ KH
 * ง NG
 * จ CH
 * ฉ CH
 * ช CH
 * ฌ CH
 * ญ Y
 * ฎ D

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

title: Portal:Thai


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User:Febby~enwikiversity/Ternopil State Medical University

user/Febby/Ternopil State Medical University


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Wikiversity:Community Review/Usurpation of usernames

Usurpation
There has been some question about how we should handle requests for usurpation, esp. in light of Single User Login. Please review the following pages and discuss below. --mikeu talk 13:14, 13 September 2009 (UTC)

 * Changing username
 * Wikiversity talk:Changing username
 * Usurpation requested

Discussion
Speaking for myself (and mikeu, I'm pretty sure), my approach to date has been to be conservative when it comes to usurpation requests, which is to say I haven't granted requests when the target account has edits. Given that there's no clear statement by the community about whether to usurp in other cases, this is the safer course since we can always do one later. Personally I don't see any pressing need to do it in cases where another user has already made edits connected with the target username.

As far as I can tell, there's 3 ways to do it:
 * 1) only allow usurping of accounts that either have no edits at all or where the current owner of the username gives explicit permission
 * 2) allow usurping of accounts which have less than a certain number of edits and/or have been inactive for a certain amount of time, or
 * 3) decide cases that don't fit the first description on a case-by-case basis using something similar to WV:CR.

I think the second way has problems, and the third way might be a bit onerous. --SB_Johnny talk 13:53, 13 September 2009 (UTC)

 * Yes, I have been very cautious in considering these requests due to the lack of a clear statement from the community. Personally, I might be inclined to support the usurpation in cases where there are no significant edits, however this can be rather subjective.  In any case, our request page has been stalled at times and the crats really need some input from everyone on how we should handle these cases.  Number #3 would mostly certainly cause stalling of our progress on deciding on these requests.  While I might tend to go with #2 I doubt we would be able to come up with a set of rules that is clear and everyone agrees upon.  --mikeu talk 14:02, 13 September 2009 (UTC)

 * Just to expand a bit on my prior comment. Option #1 seems to have wide support, though I do have concerns that it might be too strict.  I would support #3 as a sort of appeals or review process for cases that are not so clear cut.  For example, a literal interpretation of #1 would preclude usurpation in a case where an account only has a single edit that was reverted as vandalism.  As someone who clicks the button to make these changes I'd like to have a clear guideline that covers the majority of cases.  But, I do support the idea of having some flexibility in making these decisions.  --mikeu talk 21:11, 16 September 2009 (UTC)

 * I agree with number 1: Protecting existing user names of people who may some day return and continue editing is more important than giving new users exactly the user name they want. StuRat 14:58, 13 September 2009 (UTC)

 * I think that position may have made sense prior to SUL, or at least there was no good reason to muck things up; but since the implementation of SUL, it's important to look at the effect across projects because it affects editors here who want SULs and it affects editors who might come here (and some come the first time merely because of SUL). If you implement a rule like the above, a person can end up with an account that is unified throughout all but one or two projects because a user years ago made a few edits and left.  That defeats the whole purpose of SUL.  Besides, only very experienced users generally will be able to check a username across all projects for use and then be able to figure out whether particular non-English projects will allow you to usurp if it's registered.  Changing a user name once you have an SUL is not a practical option.  Sure, if you find that on one project there is an active editor by the same name then you picked the wrong name if you intend to edit there, no argument.  But, the meta page on SUL talks about a sort of superiority of claim.  Yes, it leaves that for the individual projects to define, but the implication is simply what I just stated, you can't expect to go stealing away active editor's names.  But there should be some level of discretion for what clearly appear to be abandoned accounts.  By the way, an SUL usurpation really is only relevant to older and less active accounts as active or newer editors will generally have taken the time to obtain SUL accounts by ensuring they had names that were available for SUL (or creating them automatically, thereby reserving the name on most projects).  The crats above know this, but just so it's clear to everyone else, I have an SUL usurpation request pending since last December, so you know that I have a bias.--BewareofDoug 22:26, 13 September 2009 (UTC)

 * I agree with the first approach. I think the person that registered the name locally has "superiority of claim". I think the first approach is the only way to assume good faith and prevent confusion should a person return some day. If changing a SUL username is hard then SUL should be fixed. SUL could maybe even be changed to allow usernames to be different across projects while maintaining a single login. -- dark lama  14:21, 14 September 2009 (UTC)

 * That's a great idea and maybe it should be but it's not. In the particular case that brought this here, the user has no mainspace edits, last edit of about 60 total was over 3 years ago, and the user has another account (also not used in over 3 years) which exists on multiple projects suggesting that that account is (or was) the primary account.  Does your position regarding such an account remain the same?--BewareofDoug 20:23, 18 October 2009 (UTC)

 * In general, I agree with the conservative sentiment towards #1 and #3 - at least until perhaps guidelines can be established for #2. Existing accounts should be not by usurped without permission esp. where there is editing locally and across projects e.g., I might register my kids so they have a username consistent with the rest of their online identities but they might not edit much yet. -- Jtneill - Talk - c 01:50, 21 March 2010 (UTC)

What happens to the edits by an account if it is usurped? Are they still attributed to the username along with the previous edits of the renamed user? -- Jtneill - Talk - c 01:50, 21 March 2010 (UTC)

 * The username is not the same as the account, they are attributed to the proper account. Whether the name says the same thing is another matter and depends on whether the project has its crats edit all the old posts.  On some projects they get renamed to the old account's new name. So, for example, if I were to ever successfully usurp "Doug" on this page, the current Doug account would be renamed to something like "Doug (usurped)" or "Doug (old)" or the like.  The edits would still just say Doug but they could be traced because they would show up in "Doug (old)"'s contributions not mine.  If the project wanted to, as Wikipedia has done in the past (I haven't been involved in name changes there in about a year, so I can't speak to current procedure), the Crats, admins, or a bot, could change all of Doug(old)'s posts to be signed by "User:Doug(old)".  Even the idea that only accounts without significant edits can be usurped is flawed because its stated reason was to comply with GFDL; a statement which shows a serious lack of understanding of the GFDL as well as a lack of understanding of the difference between a user's name and a user's account.--BewareofDoug 20:20, 31 August 2010 (UTC)

What if a usurpation request is received for an account with a few edits a few years ago? It is the last usurpation needed for an active user to have SUL. How do people feel about usurption in this case? -- Jtneill - Talk - c 05:52, 8 July 2010 (UTC)

 * There is no requirement to usurp before you get an SUL and SUL is automatic now and has been for over a year for new accounts. However, the SUL won't act as a Single Sign-on for projects that haven't been unified.  So, I can't merge this account with my SUL account unless the name and password are the same.  If I log onto a project that I have an SUL on and then I log onto a project that I have never been on and there is no User:Doug on that project, I will automatically assume that name.  If I log onto a project that I've never been on before directly and create an account, I'll have a new SUL on all projects.  Actually, if I go from here back to Wikipedia, I will be User:BewareofDoug.  I have unified the account across all projects to protect it, but I do not edit with it except here.--BewareofDoug 20:20, 31 August 2010 (UTC)

Practical considerations
Situation: User Y registered years ago, has no talk or user page, and has no edits. Email not enabled. User with SUL Y creates or has account X here, and requests usurpation, X -> Y. I just did this on fr.wikiversity (Usurping Abd there). Granted within one day. They did not require me to notify Y. What that would do is simply create an almost certainly useless user talk page. What has actual 'crat experience been for no-email, no-edit accounts? --Abd 01:16, 30 August 2011 (UTC)


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Flight dynamics

Flight dynamics is the science of air and space vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw (quite different from their use as Tait-Bryan angles).

Aerospace engineers develop control systems for a vehicle's orientation (attitude) about its center of mass. The control systems include actuators, which exert forces in various directions, and generate rotational forces or moments about the aerodynamic center of the aircraft, and thus rotate the aircraft in pitch, roll, or yaw. For example, a pitching moment is a vertical force applied at a distance forward or aft from the aerodynamic center of the aircraft, causing the aircraft to pitch up or down.

Roll, pitch and yaw refer to rotations about the respective axes starting from a defined equilibrium state. The equilibrium roll angle is known as wings level or zero bank angle, equivalent to a level heeling angle on a ship. Yaw is known as 'heading'. The equilibrium pitch angle in submarine and airship parlance is known as 'trim', but in aircraft, this usually refers to angle of attack, rather than orientation. However, common usage ignores this distinction between equilibrium and dynamic cases.

The most common aeronautical convention defines the roll as acting about the longitudinal axis, positive with the starboard(right) wing down. The yaw is about the vertical body axis, positive with the nose to starboard. Pitch is about an axis perpendicular to the longitudinal plane of symmetry, positive nose up.

A fixed-wing aircraft increases or decreases the lift generated by the wings when it pitches nose up or down by increasing or decreasing the angle of attack (AOA). The roll angle is also known as bank angle on a fixed wing aircraft, which usually "banks" to change the horizontal direction of flight. An aircraft is usually streamlined from nose to tail to reduce drag making it typically advantageous to keep the sideslip angle near zero, though there are instances when an aircraft may be deliberately "sideslipped" for example a slip in a fixed wing aircraft.

Coordinate systems
The position (and hence motion) of an aircraft is generally defined relative to one of 3 sets of co-ordinate systems:

 * Wind Axes
 * X Axis - Positive in the direction of the oncoming air (relative wind)
 * Y Axis - Positive to Right of X Axis, perpendicular to X Axis
 * Z Axis - Positive downwards, perpendicular to X-Y plane

 * Inertial Axes (or Body Axes) - based about aircraft CG
 * X Axis - Positive forward, through nose of aircraft
 * Y Axis - Positive to Right of X Axis, perpendicular to X Axis
 * Z Axis - Positive downwards, perpendicular to X-Y plane

 * Earth Axes
 * X Axis - Positive in the direction of North
 * Y Axis - Positive in the direction of East (perpendicular to X Axis)
 * Z Axis - Positive towards the centre of Earth (perpendicular to X-Y Plane)

For flight dynamics applications the Earth Axes are generally of minimal use, and hence will be ignored. The motions relevant to dynamic stability are usually too short in duration for the motion of the Earth itself to be considered relevant for aircraft.

In flight dynamics, pitch, roll and yaw angles measure both the absolute attitude angles (relative to the horizon/North) and changes in attitude angles, relative to the equilibrium orientation of the vehicle. These are defined as:
 * Pitch - Angle of X Body Axis (nose) relative to horizon. Also a positive (nose up) rotation about Y Body Axis
 * Roll - Angle of Y Body Axis (wing) relative to horizon. Also a positive (right wing down) rotation about X Body Axis
 * Yaw - Angle of X Body Axis (nose) relative to North. Also a positive (nose right) rotation about Z Body axis

In analysing the dynamics, we are concerned both with rotation and translation of this axis set with respect to a fixed inertial frame. For all practical purposes a local Earth axis set is used, this has X and Y axis in the local horizontal plane, usually with the x-axis coinciding with the projection of the velocity vector at the start of the motion, on to this plane. The z axis is vertical, pointing generally towards the Earth's centre, completing an orthogonal set.

In general, the body axes are not aligned with the Earth axes. The body orientation may be defined by three Euler angles, the Tait-Bryan rotations, a quaternion, or a direction cosine matrix (rotation matrix). A rotation matrix is particularly convenient for converting velocity, force, angular velocity, and torque vectors between body and Earth coordinate frames.

Body axes tend to be used with missile and rocket configurations. Aircraft stability uses wind axes in which the x-axis points along the velocity vector. For straight and level flight this is found from body axes by rotating nose down through the angle of attack.

Stability deals with small perturbations in angular displacements about the orientation at the start of the motion. This consists of two components; rotation about each axis, and angular displacements due change in orientation of each axis. The latter term is of second order for the purpose of stability analysis, and is ignored.

Design cases
In analysing the stability of an aircraft, it is usual to consider perturbations about a nominal equilibrium position. So the analysis would be applied, for example, assuming:
 * Steady level flight
 * Turn at constant speed
 * Approach and landing
 * Take off

The speed, height and trim angle of attack are different for each flight condition, in addition, the aircraft will be configured differently, e.g. at low speed flaps may be deployed and the undercarriage may be down.

Except for asymmetric designs (or symmetric designs at significant sideslip), the longitudinal equations of motion (involving pitch and lift forces) may be treated independently of the lateral motion (involving roll and yaw).

The following considers perturbations about a nominal straight and level flight path.

To keep the analysis (relatively) simple, the control surfaces are assumed fixed throughout the motion, this is stick-fixed stability. Stick-free analysis requires the further complication of taking the motion of the control surfaces into account.

Furthermore, the flight is assumed to take place in still air, and the aircraft is treated as a rigid body.

Spacecraft
Unless designed to conduct part of the mission within a planetary atmosphere, a spacecraft would generally have no discernible front or side, and no bottom unless designed to land on a surface, so reference to a 'nose' or 'wing' or even 'down' is arbitrary. On a manned spacecraft, the axes must be oriented relative to the pilot's physical orientation at the flight control station. Unmanned spacecraft may need to maintain orientation of solar cells toward the Sun, antennas toward the Earth, or cameras toward a target, so the axes will typically be chosen relative to these functions.

Longitudinal modes
It is common practice to derive a fourth order characteristic equation to describe the longitudinal motion, and then factorise it approximately into a high frequency mode and a low frequency mode. This requires a level of algebraic manipulation which most readers will doubtless find tedious, and adds little to the understanding of aircraft dynamics. The approach adopted here is to use our qualitative knowledge of aircraft behaviour to simplify the equations from the outset, reaching the same result by a more accessible route.

The two longitudinal motions (modes) are called the short period pitch oscillation (SSPO), and the phugoid.

Short-period pitch oscillation
A short input (in control systems terminology an impulse) in pitch (generally via the elevator in a standard configuration fixed wing aircraft) will generally lead to overshoots about the trimmed condition. The transition is characterised by a damped simple harmonic motion about the new trim. There is very little change in the trajectory over the time it takes for the oscillation to damp out.

Generally this oscillation is high frequency (hence short period) and is damped over a period of a few seconds. A real-world example would involve a pilot selecting a new climb attitude, for example 5º nose up from the original attitude. A short, sharp pull back on the control column may be used, and will generally lead to oscillations about the new trim condition. If the oscillations are poorly damped the aircraft will take a long period of time to settle at the new condition, potentially leading to Pilot-induced oscillation. If the short period mode is unstable it will generally be impossible for the pilot to safely control the aircraft for any period of time.

This damped harmonic motion is called the short period pitch oscillation, it arises from the tendency of a stable aircraft to point in the general direction of flight. It is very similar in nature to the weathercock mode of missile or rocket configurations. The motion involves mainly the pitch attitude $$\theta$$ (theta) and incidence $$\alpha$$ (alpha). The direction of the velocity vector, relative to inertial axes is $$\theta-\alpha$$. The velocity vector is:

 * $$u_f=U\cos(\theta-\alpha)$$
 * $$w_f=U\sin(\theta-\alpha)$$

where $$u_f$$,$$ w_f$$ are the inertial axes components of velocity. According to Newton's Second Law, the accelerations are proportional to the forces, so the forces in inertial axes are:

 * $$X_f=m\frac{du_f}{dt}=m\frac{dU}{dt}\cos(\theta-\alpha)-mU\frac{d(\theta-\alpha)}{dt}\sin(\theta-\alpha)$$
 * $$Z_f=m\frac{dw_f}{dt}=m\frac{dU}{dt}\sin(\theta-\alpha)+mU\frac{d(\theta-\alpha)}{dt}\cos(\theta-\alpha)$$

where m is the mass. By the nature of the motion, the speed variation $$m\frac{dU}{dt}$$ is negligible over the period of the oscillation, so:

 * $$X_f= -mU\frac{d(\theta-\alpha)}{dt}\sin(\theta-\alpha)$$
 * $$Z_f=mU\frac{d(\theta-\alpha)}{dt}\cos(\theta-\alpha)$$

But the forces are generated by the pressure distribution on the body, and are referred to the velocity vector. But the velocity (wind) axes set is not an inertial frame so we must resolve the fixed axes forces into wind axes. Also, we are only concerned with the force along the z-axis:

 * $$Z=-Z_f\cos(\theta-\alpha)+X_f\sin(\theta-\alpha)$$

Or:
 * $$Z=-mU\frac{d(\theta-\alpha)}{dt}$$

In words, the wind axes force is equal to the centripetal acceleration.

The moment equation is the time derivative of the angular momentum:
 * $$M=B\frac{d^2 \theta}{dt^2}$$

where M is the pitching moment, and B is the moment of inertia about the pitch axis. Let: $$\frac{d\theta}{dt}=q$$, the pitch rate. The equations of motion, with all forces and moments referred to wind axes are, therefore:
 * $$\frac{d\alpha}{dt}=q+\frac{Z}{mU}$$
 * $$\frac{dq}{dt}=\frac{M}{B}$$

We are only concerned with perturbations in forces and moments, due to perturbations in the states $$\alpha$$ and q, and their time derivatives. These are characterised by stability derivatives determined from the flight condition. The possible stability derivatives are:

 * $$Z_\alpha$$ Lift due to incidence, this is negative because the z-axis is downwards whilst positive incidence causes an upwards force.

 * $$Z_q$$ Lift due to pitch rate, arises from the increase in tail incidence, hence is also negative, but small compared with $$Z_\alpha$$.

 * $$M_\alpha$$ Pitching moment due to incidence - the static stability term. Static stability requires this to be negative.

 * $$M_q$$ Pitching moment due to pitch rate - the pitch damping term, this is always negative.

Since the tail is operating in the flowfield of the wing, changes in the wing incidence cause changes in the downwash, but there is a delay for the change in wing flowfield to affect the tail lift, this is represented as a moment proportional to the rate of change of incidence:

 * $$M_\dot\alpha$$

Increasing the wing incidence without increasing the tail incidence produces a nose up moment, so $$M_\dot\alpha$$ is expected to be positive.

The equations of motion, with small perturbation forces and moments become:

 * $$\frac{d\alpha}{dt}=\left(1+\frac{Z_q}{mU}\right)q+\frac{Z_\alpha}{mU}\alpha$$

 * $$\frac{dq}{dt}=\frac{M_q}{B}q+\frac{M_\alpha}{B}\alpha+\frac{M_\dot\alpha}{B}\dot\alpha$$

These may be manipulated to yield as second order linear differential equation in $$\alpha$$:

 * $$\frac{d^2\alpha}{dt^2}-\left(\frac{Z_\alpha}{mU}+\frac{M_q}{B}+(1+\frac{Z_q}{mU})\frac{M_\dot\alpha}{B}\right)\frac{d\alpha}{dt}+\left(\frac{Z_\alpha}{mU}\frac{M_q}{B}-\frac{M_\alpha}{B}(1+\frac{Z_q}{mU})\right)\alpha=0 $$

This represents a damped simple harmonic motion.

We should expect $$\frac{Z_q}{mU}$$ to be small compared with unity, so the coefficient of $$\alpha$$ (the 'stiffness' term) will be positive, provided $$M_\alpha<\frac{Z_\alpha}{mU}M_q$$. This expression is dominated by $$M_\alpha$$, which defines the longitudinal static stability of the aircraft, it must be negative for stability. The damping term is reduced by the downwash effect, and it is difficult to design an aircraft with both rapid natural response and heavy damping. Usually, the response is underdamped but stable.

Phugoid
If the stick is held fixed, the aircraft will not maintain straight and level flight, but will start to dive, level out and climb again. It will repeat this cycle until the pilot intervenes. This long period oscillation in speed and height is called the phugoid mode. This is analysed by assuming that the SSPO performs its proper function and maintains the angle of attack near its nominal value. The two states which are mainly affected are the climb angle $$\gamma$$ (gamma) and speed. The small perturbation equations of motion are:

 * $$mU\frac{d\gamma}{dt}=-Z$$

which means the centripetal force is equal to the perturbation in lift force.

For the speed, resolving along the trajectory:

 * $$m\frac{du}{dt}=X-mg\gamma$$

where g is the acceleration due to gravity at the earths surface. The acceleration along the trajectory is equal to the net x-wise force minus the component of weight. We should not expect significant aerodynamic derivatives to depend on the climb angle, so only $$X_u$$ and $$Z_u$$ need be considered. $$X_u$$ is the drag increment with increased speed, it is negative, likewise $$Z_u$$ is the lift increment due to speed increment, it is also negative because lift acts in the opposite sense to the z-axis.

The equations of motion become:
 * $$ mU\frac{d\gamma}{dt}=-Z_u u$$
 * $$ m\frac{du}{dt}=X_u u -mg\gamma$$

These may be expressed as a second order equation in climb angle or speed perturbation:
 * $$\frac{d^2u}{dt^2}-\frac{X_u}{m}\frac{du}{dt}-\frac{Z_ug}{mU}u=0$$

Now lift is very nearly equal to weight:
 * $$Z=\frac{1}{2}\rho U^2 c_L S_w=W$$

where $$\rho$$ is the air density, $$S_w$$ is the wing area, W the weight and $$c_L$$ is the lift coefficient (assumed constant because the incidence is constant), we have, approximately:

 * $$Z_u=\frac{2W}{U}=\frac{2mg}{U}$$

The period of the phugoid, T, is obtained from the coefficient of u:

 * $$\frac{2\pi}{T}=\sqrt{\frac{2g^2}{U^2}}$$

Or:
 * $$T=\frac{2\pi U}{\sqrt{2}g}$$

Since the lift is very much greater than the drag, the phugoid is at best lightly damped. A propeller with fixed speed would help. Heavy damping of the pitch rotation or a large rotational inertia increase the coupling between short period and phugoid modes, so that these will modify the phugoid.

Lateral modes
With a symmetrical rocket or missile, the directional stability in yaw is the same as the pitch stability; it resembles the short period pitch oscillation, with yaw plane equivalents to the pitch plane stability derivatives. For this reason pitch and yaw directional stability are collectively known as the 'weathercock' stability of the missile.

Aircraft lack the symmetry between pitch and yaw, so that directional stability in yaw is derived from a different set of stability derivatives, The yaw plane equivalent to the short period pitch oscillation, which describes yaw plane directional stability is called Dutch roll. Unlike pitch plane motions, the lateral modes involve both roll and yaw motion.

Dutch roll
It is customary to derive the equations of motion by formal manipulation in what, to the engineer, amounts to a piece of mathematical sleight of hand. The current approach follows the pitch plane analysis in formulating the equations in terms of concepts which are reasonably familiar.

Applying an impulse via the rudder pedals should induce Dutch roll, which is the oscillation in roll and yaw, with the roll motion lagging yaw by a quarter cycle, so that the wing tips follow elliptical paths with respect to the aircraft.

The yaw plane translational equation, as in the pitch plane, equates the centripetal acceleration to the side force.

 * $$\frac{d\beta}{dt}=\frac{Y}{mU}-r$$

where $$\beta$$ (beta) is the sideslip angle, Y the side force and r the yaw rate.

The moment equations are a bit trickier. The trim condition is with the aircraft at an angle of attack with respect to the airflow, The body x-axis does not align with the velocity vector, which is the reference direction for wind axes. In other words, wind axes are not principal axes (the mass is not distributed symmetrically about the yaw and roll axes). Consider the motion of an element of mass in position -z,x in the direction of the y-axis, i.e. into the plane of the paper.

If the roll rate is p, the velocity of the particle is:

 * $$v=-pz+xr$$

Made up of two terms, the force on this particle is first the proportional to rate of v change, the second is due to the change in direction of this component of velocity as the body moves. The latter terms gives rise to cross products of small quantities (pq,pr,qr), which are later discarded. In this analysis, they are discarded from the outset for the sake of clarity. In effect, we assume that the direction of the velocity of the particle due to the simultaneous roll and yaw rates does not change significantly throughout the motion. With this simplifying assumption, the acceleration of the particle becomes:

 * $$\frac{dv}{dt}=-\frac{dp}{dt}z+\frac{dr}{dt}x$$

The yawing moment is given by:

 * $$\delta m x \frac{dv}{dt}=-\frac{dp}{dt}xz\delta m + \frac{dr}{dt}x^2\delta m $$

There is an additional yawing moment due to the offset of the particle in the y direction:$$\frac{dr}{dt}y^2\delta m$$

The yawing moment is found by summing over all particles of the body:

 * $$N=-\frac{dp}{dt}\int xz dm +\frac{dr}{dt}\int x^2 + y^2 dm =-E\frac{dp}{dt}+C\frac{dr}{dt}$$

where N is the yawing moment, E is a product of inertia, and C is the moment of inertia about the yaw axis. A similar reasoning yields the roll equation:

 * $$L=A\frac{dp}{dt}-E\frac{dr}{dt}$$

where L is the rolling moment and A the roll moment of inertia.

Lateral and longitudinal stability derivatives
The states are $$\beta$$ (sideslip),r (yaw rate) and p (roll rate), with moments N (yaw) and L (roll), and force Y (sideways). There are nine stability derivatives relevant to this motion, the following explains how they originate. However a better intuitive understanding is to be gained by simply playing with a model aeroplane, and considering how the forces on each component are affected by changes in sideslip and angular velocity:

 * $$Y_\beta$$ Side force due to side slip (in absence of yaw).

Sideslip generates a sideforce from the fin and the fuselage. In addition, if the wing has dihedral, side slip at a positive roll angle increases incidence on the starboard wing and reduces it on the port side, resulting in a net force component directly opposite to the sideslip direction. Sweep back of the wings has the same effect on incidence, but since the wings are not inclined in the vertical plane, backsweep alone does not affect $$Y_\beta$$. However, anhedral may be used with high backsweep angles in high performance aircraft to offset the wing incidence effects of sideslip. Oddly enough this does not reverse the sign of the wing configuration's contribution to $$Y_\beta$$ (compared to the dihedral case).

 * $$Y_p$$ Side force due to roll rate.

Roll rate causes incidence at the fin, which generates a corresponding side force. Also, positive roll (starboard wing down) increases the lift on the starboard wing and reduces it on the port. If the wing has dihedral, this will result in a side force momentarily opposing the resultant sideslip tendency. Anhedral wing and or stabiliser configurations can cause the sign of the side force to invert if the fin effect is swamped.

 * $$Y_r$$ Side force due to yaw rate.

Yawing generates side forces due to incidence at the rudder, fin and fuselage.

 * $$N_\beta$$ Yawing moment due to sideslip forces.

Sideslip in the absence of rudder input causes incidence on the fuselage and empennage, thus creating a yawing moment counteracted only by the directional stiffness which would tend to point the aircraft's nose back into the wind in horizontal flight conditions. Under sideslip conditions at a given roll angle $$N_\beta$$ will tend to point the nose into the sideslip direction even without rudder input, causing a downward spiralling flight.

 * $$N_p$$ Yawing moment due to roll rate.

Roll rate generates fin lift causing a yawing moment and also differentially alters the lift on the wings, thus affecting the induced drag contribution of each wing, causing a (small) yawing moment contribution. Positive roll generally causes positive $$N_p$$ values unless the empennage is anhedral or fin is below the roll axis. Lateral force components resulting from dihedral or anhedral wing lift differences has little effect on $$N_p$$ because the wing axis is normally closely aligned with the centre of gravity.

 * $$N_r$$ Yawing moment due to yaw rate.

Yaw rate input at any roll angle generates rudder, fin and fuselage force vectors which dominate the resultant yawing moment. Yawing also increases the speed of the outboard wing whilst slowing down the inboard wing, with corresponding changes in drag causing a (small) opposing yaw moment. $$N_r$$ opposes the inherent directional stiffness which tends to point the aircraft's nose back into the wind and always matches the sign of the yaw rate input.

 * $$L_\beta$$ Rolling moment due to sideslip.

A positive sideslip angle generates empennage incidence which can cause positive or negative roll moment depending on its configuration. For any non-zero sideslip angle dihedral wings causes a rolling moment which tends to return the aircraft to the horizontal, as does back swept wings. With highly swept wings the resultant rolling moment may be excessive for all stability requirements and anhedral could be used to offset the effect of wing sweep induced rolling moment.

 * $$L_r$$ Rolling moment due to yaw rate.

Yaw increases the speed of the outboard wing whilst reducing speed of the inboard one, causing a rolling moment to the inboard side. The contribution of the fin normally supports this inward rolling effect unless offset by anhedral stabiliser above the roll axis (or dihedral below the roll axis).

 * $$L_p$$ Rolling moment due to roll rate.

Roll creates counter rotational forces on both starboard and port wings whilst also generating such forces at the empennage. These opposing rolling moment effects have to be overcome by the aileron input in order to sustain the roll rate. If the roll is stopped at a non-zero roll angle the $$L_\beta$$ upward rolling moment induced by the ensueing sideslip should return the aircraft to the horizontal unless exceeded in turn by the downward $$L_r$$ rolling moment resulting from sideslip induced yaw rate. Longitudinal stability could be ensured or improved by minimizing the latter effect.

Equations of motion
Since Dutch roll is a handling mode, analogous to the short period pitch oscillation, we shall ignore any effect it might have on the trajectory. The body rate r is made up of the rate of change of sideslip angle and the rate of turn. Taking the latter as zero, because we assume no effect on the trajectory, we have, for the limited purpose of studying the Dutch roll:

 * $$\frac{d\beta}{dt}= -r$$

The yaw and roll equations, with the stability derivatives become:

 * $$C\frac{dr}{dt}-E\frac{dp}{dt}=N_\beta \beta - N_r \frac{d\beta}{dt} + N_p p$$ (yaw)

 * $$A\frac{dp}{dt}-E\frac{dr}{dt}=L_\beta \beta - L_r \frac{d\beta}{dt} + L_p p$$ (roll)

The inertial moment due to the roll acceleration is considered small compared with the aerodynamic terms, so the equations become:

 * $$-C\frac{d^2\beta}{dt^2} = N_\beta \beta - N_r \frac{d\beta}{dt} + N_p p$$
 * $$E\frac{d^2\beta}{dt^2} = L_\beta \beta - L_r \frac{d\beta}{dt} + L_p p$$

This becomes a second order equation governing either roll rate or sideslip:

 * $$\left(\frac{N_p}{C}\frac{E}{A}-\frac{L_p}{A}\right)\frac{d^2\beta}{dt^2}+

\left(\frac{L_p}{A}\frac{N_r}{C}-\frac{N_p}{C}\frac{L_r}{A}\right)\frac{d\beta}{dt}- \left(\frac{L_p}{A}\frac{N_\beta}{C}-\frac{L_\beta}{A}\frac{N_p}{C}\right)\beta = 0$$

The equation for roll rate is identical. But the roll angle, $$\phi$$ (phi)is given by:

 * $$\frac{d\phi}{dt}=p$$

If p is a damped simple harmonic motion, so is $$\phi$$, but the roll must be in quadrature with the roll rate, and hence also with the sideslip. The motion consists of oscillations in roll and yaw, with the roll motion lagging 90 degrees behind the yaw. The wing tips trace out elliptical paths.

Stability requires the 'stiffness' and 'damping' terms to be positive. These are:

 * $$\frac{\frac{L_p}{A}\frac{N_r}{C}-\frac{N_p}{C}\frac{L_r}{A}}

{\frac{N_p}{C}\frac{E}{A}-\frac{L_p}{A}}$$ (damping)

 * $$\frac{\frac{L_\beta}{A}\frac{N_p}{C}-\frac{L_p}{A}\frac{N_\beta}{C}}

{\frac{N_p}{C}\frac{E}{A}-\frac{L_p}{A}}$$ (stiffness)

The denominator is dominated by $$L_p$$, the roll damping derivative, which is always negative, so the denominators of these two expressions will be positive.

Considering the 'stiffness' term: $$-L_p N_\beta$$ will be positive because $$L_p$$ is always negative and $$N_\beta$$ is positive by design. $$L_\beta$$ is usually negative, whilst $$N_p$$ is positive. Excessive dihedral can de-stabilise the Dutch roll, so configurations with highly swept wings require anhedral to offset the wing sweep contribution to $$L_\beta$$.

The damping term is dominated by the product of the roll damping and the yaw damping derivatives, these are both negative, so their product is positive. The Dutch roll should therefore be damped.

The motion is accompanied by slight lateral motion of the centre of gravity and a more 'exact' analysis will introduce terms in $$Y_\beta$$ etc. In view of the accuracy with which stability derivatives can be calculated, this is an unnecessary pedantry, which serves to obscure the relationship between aircraft geometry and handling, which is the fundamental objective of this article.

Roll subsidence
Jerking the stick sideways and returning it to centre causes a net change in roll orientation.

The roll motion is characterized by an absence of natural stability, there are no stability derivatives which generate moments in response to the inertial roll angle. A roll disturbance induces a roll rate which is only cancelled by pilot or autopilot intervention. This takes place with insignificant changes in sideslip or yaw rate, so the equation of motion reduces to:

 * $$A\frac{dp}{dt}=L_p p.$$

$$L_p$$ is negative, so the roll rate will decay with time. The roll rate reduces to zero, but there is no direct control over the roll angle.

Spiral mode
Simply holding the stick still, when starting with the wings near level, an aircraft will usually have a tendency to gradually veer off to one side of the straight flightpath. This is the (slightly unstable) spiral mode. The opposite holds for a stable spiral mode. The spiral mode is so-named because when it is slightly unstable, and the controls are not moved, the aircraft will tend to increase its bank angle slowly at first, then ever faster. The resulting path through the air is a continuously tightening and ever more rapidly descending spiral. An unstable spiral mode is common to most aircraft. It is not dangerous because the times to double the bank angle are large compared to the the pilot's ability to respond and correct errors with aileron inputs.

When the spiral mode is stable, it behaves in a way opposite to the exponential divergence of the unstable mode. The stable spiral mode, when starting with the wings at a moderate bank angle, will return to near wings level, first quickly, then more slowly. When the spiral mode is stable and starting at a moderate bank angle, the spiral nature of the flight path is not as obvious. This is because usually only a fraction of a turn is made while the wings are not fully level. The turning starts out (relatively) tight, then becomes less and less so as the wings become more level.

The divergence rate of the unstable spiral mode will be roughly proportional to the roll angle itself (i.e. roughly exponential growth). The convergence rate of the stable spiral mode will be roughly proportional to the roll angle itself (i.e. roughly exponential decay).

Spiral mode trajectory
In studying the trajectory, it is the direction of the velocity vector, rather than that of the body, which is of interest. The direction of the velocity vector when projected on to the horizontal will be called the track, denoted $$\mu$$ (mu). The body orientation is called the heading, denoted $$\psi$$ (psi). The force equation of motion includes a component of weight:

 * $$\frac{d\mu}{dt}=\frac{Y}{mU} + \frac{g}{U}\phi$$

where g is the gravitational acceleration, and U is the speed.

Including the stability derivatives:

 * $$\frac{d\mu}{dt}=\frac{Y_\beta}{mU}\beta + \frac {Y_r}{mU}r + \frac{Y_p}{mU}p + \frac{g}{U}\phi$$

Roll rates and yaw rates are expected to be small, so the contributions of $$Y_r$$ and $$Y_p$$ will be ignored.

The sideslip and roll rate vary gradually, so their time derivatives are ignored. The yaw and roll equations reduce to:

 * $$N_\beta \beta + N_r\frac{d\mu}{dt} + N_p p = 0$$ (yaw)

 * $$L_\beta \beta + L_r\frac{d\mu}{dt} + L_p p = 0$$ (roll)

Solving for $$\beta$$ and p:

 * $$\beta=\frac{(L_r N_p - L_p N_r)}{(L_p N_\beta - N_p L_\beta)}\frac{d\mu}{dt}$$

 * $$p=\frac{(L_\beta N_r - L_r N_\beta)}{(L_p N_\beta - N_p L_\beta)}\frac{d\mu}{dt}$$

Substituting for sideslip and roll rate in the force equation results in a first order equation in roll angle:

 * $$\frac{d\phi}{dt}=mg\frac{(L_\beta N_r - N_\beta L_r)}{mU(L_p N_\beta - N_p L_\beta)-Y_\beta(L_r N_p - L_p N_r)}\phi$$

This is an exponential growth or decay, depending on whether the coefficient of $$\phi$$ is positive or negative. The denominator is usually negative, which requires $$L_\beta N_r > N_\beta L_r$$ (both products are positive). This is in direct conflict with the Dutch roll stability requirement, and it is difficult to design an aircraft for which both the Dutch roll and spiral mode are inherently stable.

Since the spiral mode has a long time constant, the pilot can intervene to effectively stabilise it, but an aircraft with an unstable Dutch roll would be difficult to fly. It is usual to design the aircraft with a stable Dutch roll mode, but slightly unstable spiral mode.

title: Flight dynamics


text:
Wikiversity:Community Review/Multipage image upload form

multipage upload form proposal
It seems that there are two issues that we need to decide. The first is the question of a multipage upload form, which requires a change to the Wikiversity MediaWiki installation. The second is the content of those forms, or a change to our existing single page form if we decide not to go with multipage. There seems to be some support for some kind of multipage form, though we need to discuss the contents in more detail. Let's discuss below the first point about multipage upload forms. Please indicate if you agree or disagree that we should pursue this. The change that we are talking about is to add  to the Mediawiki installation which will allow us to create multipage upload forms that explain the various license options. Once we choose between keeping/modifying the existing one page form or the multipage, we can than start discussing the content, choices and wording of the text. --mikeu talk 14:06, 23 August 2009 (UTC)

 * Please see the comment from Darklama below. We could have both a multipage and a simpler single page.  This is not really a either/or question as I might have suggested above.  The question that we are asking below is if you support or oppose adding the multipage option to wikiversity.  Later we will draft the content of the forms for review by the community.  --mikeu talk 17:52, 13 September 2009 (UTC)

 * - the single page form is too limiting and (in the current state) too confusing. Switching to multipage will allow much greater flexibility and ease of use, esp. for newcomers to wikiversity.  --mikeu talk 14:09, 23 August 2009 (UTC)
 * - absolutely, we're way behind the curve on this. --SB_Johnny talk 14:14, 23 August 2009 (UTC)
 * - but with conditions & reservations:
 * - How good of a repository is Wikiversity compared to the Commons, anyway? I think the smart thing to do is direct uploads to the Commons by default if that can be done. Wikiversity could have a buffer repository for developing original media and images that go to the commons when finished. Wikiversity should develop a culture of originality and resourceful adaptation. That would leave Wikiversity's repository for Fair Use media and images only... and we would need a mechanism for approving these before anyone even thinks of uploading them. Fair Use media and images reside elsewhere on the web and can be linked to for review though a Request for comments process of some sort. I don't know the answer, but I don't like to see stuff uploaded then deleted. I'd rather issues be resolved before they become issues. My $.02 worth. CQ 15:31, 23 August 2009 (UTC)
 * I agree that a large percentage of our uploads would be better at commons. My feeling is that having a multipage upload form could allow us to steer Free Content License works to commons, while still allowing fair use uploads here.  There might also be situtations where a large number of uploads of similar images for a learning project could be seen as duplicates at commons, and therefore deleted.  But, that is a topic for another thread.  First, we need to make a simple decision on single page vs. multipage upload forms.  I think that the multipage form would allow us the flexibility to implement your suggestion, or other suggestions that might be proposed.  The current single page form limits our ability to ditinguish by license type, which is the first step in directing people to the best place for the upload.  --mikeu talk 15:40, 23 August 2009 (UTC)
 * In fact; HIGHLY support (10 on a scale of 0-10) because I HATE having to upload files one by one. Also, I think this should apply universally on all the wikis, ESPECIALLY commons. Deathgleaner 20:06, 28 August 2009 (UTC)
 * This change to the upload form would still require uploading files one by one. I'm not sure if there is any way to allow multiple uploads.  --mikeu talk 20:23, 28 August 2009 (UTC)
 * Both an upload form with all options like now and different upload forms with narrower scope is possible, this isn't really a single vs multiplepage issue. This approach would provides more choices -- dark lama  14:49, 13 September 2009 (UTC)
 * Although I appreciate the brevity of the form, as it stands today, it isn't really all that easy to bend it to fit the exingencies of complex licensing options.--Graeme E. Smith 22:05, 21 September 2009 (UTC)
 * It's especially important in an academic site like this one, because materials commonly fill more than one page. --AFriedman 05:55, 19 October 2009 (UTC)
 * the ability to improve the upload process whilst noting that Commons is a better place for free images so a revised upload process should, in my view, strongly encourage freely licensed images to be uploaded to Commons. Adambro 12:59, 14 March 2010 (UTC)

Move to close
I think it's time to make the bugzilla request. --SB_Johnny talk 10:49, 27 October 2009 (UTC)

Agree, it doesn't look like there is anyone oposed. --mikeu talk 13:57, 27 October 2009 (UTC)

 * Was there a request made for this? Adambro 20:31, 13 March 2010 (UTC)

 * Not that I can tell. Go for it! --SB_Johnny talk 12:29, 14 March 2010 (UTC)

 * Will do. Adambro 12:59, 14 March 2010 (UTC)
 * ✅ 22833. Adambro 13:28, 14 March 2010 (UTC)
 * 22833 is now resolved, just need to work out how to use it and of course how we actually want to use it. Adambro 21:29, 15 March 2010 (UTC)


text:
Votian/Imperfect Tense

== Imperfect tense ==

Personal endings

 * The very same endings of the first and second person are used in all moods and tenses.
 * Only the third person of singular is different from the present tense and has no marker at all in the imperfect tense.
 * The third person of plural has in the imperfect tense the same ending as in the present tense, even though it is derived from a suffix of present participle with a plural nominative marker t.
 * Thus according to consonant gradation principles the third person may occur only in the strong grade both in plural and singular e.g. e̮saB ('She buys.') > e̮ssi ('She bought.'), annaB ('She gives.') > anti ('She gave.' in Liivtšülä dialect - explained below), tetševäD ('They do (it).') > tetšiväD ('They did (it).'), pake̮ne̮-vaD ('They run away.') > pake̮ni-vaD ('They ran away.'), because these morphemes can never close the preceding syllable.
 * All those endings follow the vowel harmony rules  like in the present tense e.g. saitta ('You (in plural) got (it).') vs. süntüzittä ('You (in plural) were born.').

Past tense marker
The past tense marker was -i-, but it is less obvious now after numerous sound changes.

Pronunciation

 * Long vowels and i melt together into diphthongs e.g. sāmma ('We get (it).') > saimma ('We got (it).').
 * Some of them have changed their quality.
 * E.g. ȫ + -i- > ei: lȫn ('I (do) hit.') > lein ('I (dit) hit.').
 * E.g. ǖ̄ + -i- > öi:  mǖmmä ('We sell.') >  möi ('He sold.' in Alutaguse dialects ).
 * (In some dialects all the long mid vowels ē, ō,  have been diphthongized to ie, uo, üö elswhere e.g. lüön ('I (do) hit.') > lein ('I (dit) hit.').)

 * Short vowels and i melt together into a single short vowel.
 * E.g. e + -i- > i: pezemmä ('We wash.') > pezimmä ('We washed.').
 * E.g. e̮ + -i- > i: ne̮ise̮vaD ('They rise.') > ne̮isivaD ('They rose.').
 * E.g. ä + -i- > i: püvvän ('I catch.') > püvvin ('I caught.' in Mati dialect) vs pǖzin ('I caught.' in Lempola dialect - explained below).
 * E.g. a + -i- > i: ve̮ittavaD ('They win.') > ve̮ittivaD ('They won.'), e̮saB ('She buys.') >  e̮ssi ('She bought.'), annaB ('She gives.') > anti ('She gave.' in Liivtšülä dialect).
 * The cases above may produce long i in certain words and dialects e.g. murraB ('He breaks.') > murtī ('He broke.' in Mati dialect), lentī  ('She flew.'), pake̮ne̮vaD ('They run away.') > pake̮nīvaD ('They ran away.' in Lempola dialect).
 * The long i is characteristic to words of long stem-vowel (usually derived with -tta) e.g.  kummartāB ('He bows.') > kummartī ('He bowed.'), (h)üppǟB  ('She jumps.') > (h)üppī  ('She jumped.').
 * a + -i- > e̮ in the second syllable, if the first syllable has a  (in the majority of the dialects) : e.g. ajavaD ('They drive (away).') > aje̮vaD ('They drove (away).').
 * o + -i- > e̮: e.g. sioB ('He ties.') > site̮ ('He tied.'), tahoB ('He wants.') > tahte̮ ('He wanted.'). This occurres only with the third person of singular though and all the other personal endings follow zi as explained below.
 * o + -i- > o (in other dialects): e.g. tahoB ('He wants.') > tahto ('He wanted.'). This occurres only with the third person of singular though and all the other personal endings follow zi as explained below.
 * u + -i- > u: e.g. kutsuB ('He calls.') > kuttsu ('He called.'). This occurres only with the third person of singular though and all the other personal endings follow zi as explained below.
 * ü + -i- > ü: e.g. sünnüB ('He will be born.') > süntü ('He was born.'). This occurres only with the third person of singular though and all the other personal endings follow zi as explained below.
 * i + -i- > i: e.g. ehiB ('He decorates.') > ehti ('He decorated.'). This occurres only with the third person of singular though and all the other personal endings follow zi as explained below.
 * Except the third person of singular, all the other personal endings follow zi after o, u, ü and i-stems. All those forms may occur only in the strong grade, because this morpheme can never close the preceding syllable.
 * o + -i- > zi: e.g. se̮ise̮ ('He stood.') ~ se̮isoziD ('You stood.').
 * u + -i- > zi: e.g. kuttsu ('He called.') ~ kuttsuzin ('I called.').
 * ü + -i- > zi: e.g. süntü ('He was born.') ~ süntüzittä ('You (in plural) were born.').
 * i + -i- > zi: e.g. ehti ('He decorated.') ~ ehtiziväD ('They decorated.').
 * The metanalytic zi morpheme comes originally from -t stems, which had to undergo a regular Finnic sound change  *ti > si : e.g. viskān ('I throw.') > viskazin ('I threw.')  < * viskasin < viskat+i+n.
 * Those stems may have *at + -i- > e̮ for the third person of singular : e.g. viske̮ ('He threw.').
 * Nevertheless the regular form should be simply zi with no personal ending : e.g. suvāB ('He loves.') > suvaz(i) ('He loved.'). The final i may be dropped.

Morphophonology

 * All the personal endings follow the vowel harmony rules  like in the present tense e.g. saitta ('You (in plural) got (it).') vs. süntüzittä ('You (in plural) were born.').
 * According to consonant gradation principles the third person may occur only in the strong grade both in plural and singular e.g. e̮saB ('She buys.') > e̮ssi ('She bought.'), annaB ('She gives.') > anti ('She gave.'), tetševäD ('They do (it).') > tetšiväD ('They did (it).'), pake̮ne̮-vaD ('They run away.') > pake̮ni-vaD ('They ran away.'), because these morphemes can never close the preceding syllable.
 * All the other persons are always in the same grade as the singular of the second person imperative and in a grade opposite to any other suffixal imperative form caused by consonant gradation in stems e.g. jättägō ('Let him leave (it)!') vs. jätin ('I left (it).') or page̮t-kā ('Escape!') vs. pake̮n-ī-D ('You escaped.').
 * All the forms with zi morpheme may occur only in the strong grade, because this morpheme can never close the preceding syllable.

Dialectal alternatives

 * 1) In Alutaguse dialects
 * 2) The local counterpart (si) of zi-morpheme has intruded into every conjugation now (influenced by  Mid Estonian dialect) including the third person of singular. It's characteristic to  heavy  two-syllable -a, -ä, -e-stems.
 * 3) E.g. :  kitkesimma ('We plucked.'), laskes ('He let (down).'), tunDes ~ tunDas ('He felt.'), jättäsimmä ('We left (it).'), kanDasin ('I carried.'), karttas ('She was afraid.'), luottasin ('I hoped.'), nīttasimma ('We mowed.'), paistas ('It seemed.'), tappas ('It killed.'), toittasin ('I fed.'), te̮stas ('It lifted.'), maksas ('She paid.'), kurttasin ('I complained.'), e̮stasitta ('You bought.'), kastas ('He watered.'), laulas ('He sang.'), sāttas ('He sent.'), tahtas ('He wanted.' in Iisaku dialect);
 * 4) The original system has been preserved in limited verbs only.
 * 5) E.g. most of the  monosyllable vowel-stems :  vei ('He took (it somewhere).') ~ vein ('I took (it somewhere).');
 * 6) most of the  consonant-stems :  panin ('I (did) put (it somewhere).'), olin ('I was.'), tulin ('I came.'), meni ('She went.'), surivaD ('They died.'), kūli ('She heard.'), me̮tlin ('I thought.'), e̮mblin ('I sewed.'), ütlin ('I said.'), kauplit ('You traded.'), rītlivaD ('They quarreled.'), vihtliväD ('They whisked (in sauna).'), vihelsiväD ('They whisked (in sauna).'), tuisima ('We rose.'), siGini ('It propagated.');
 * 7) näGin ('I saw.' instead of näin), teGin ('I did.' instead of tein), suk̆in ('I combed.'), lukin ('I (did) read (it).'), lasin ~ lasima ('I ~ we (did) let down.'), which do not follow consonant gradation principles any more;
 * 8) some of the  -a  and  ä-stems : tahi ('She wanted.'), aiD ('They drove (away).'), jaksivaD ('They had strenght enough to (do something).'), jättimä ('We left (something).'), karDin ('I was afraid.'), keiDimä ('We boiled.'), laulivaD ('They sang.'), ve̮ttin ('I took.'), süöDima ('We fed.');
 * 9) verbs derived with -tta on a long vowel or sonorant had to undergo a regular Finnic sound change  *ti > si: e.g. je̮usivad ('They had strenght enough to (do something).')  < * je̮ut+i+vat < * je̮uta+i+vat, leisin ('I found.'), ne̮usima ('We demanded.'), oisin ('I hold.'), pǖsima ('We caught.'), tiesit̆ta ~ tiasitta ('You knew.'), ǖsiväD ('They shouted.').
 * 10) Sometimes the result has a new secondary t between n and s: e.g. an(t)s ~ anDas ('She gave.'),  küntsin ~ künDäsin ('I plowed.'),  len(t)si ~ lenDi ('He flew.').
 * 11) The final i of the third person of singular is usually dropped excluding  light  two-syllable stems : e.g. je̮us ('She had strenght enough to (do something).'),  te̮mps ('She pulled.'),  püörs ('He turned.'),  künts ('He plowed.'),  peks ~ peksäs ('He (did) beat.'),  leis ~ leitäs ('She found.'),  ois ~ oitas ('She hold.'),  ties ~ tias ~ tieDäs in Lüganuse dialect ~ tiaDas in Iisaku dialect ('She hold.'), tuis ~ tuises ('He rose.'), ammust ('He bit.'), me̮ttel ('She thought.'), kauppel ('She traded.'), nuhtel ('She penalized.'), rīttel ('He quarreled.'), vihtel ('She whisked (in sauna).'), üttel ('She said.'), juoks(i) ('She ran.'), tappas ~ tap̄ ('She killed.'), luki ('She (did) read (it).').
 * 12) The third person of plural may use a bare plural nominative marker t (influenced by  Mid Estonian dialect) and thus become not distinguishable from the second person of singular e.g. aiD ('They drove (away).' instead of ajivaD ).

=== Other Finnic dialects ===

The first person of singular
 * Standard Finnish : lu-i-n ('I read.')
 * Vesjegonski Karelian dialects : luv-i-n ('I read.')
 * Vepsian dialects : lug-i-ń ('I read.')
 * Ingrian dialects : lu-i-n ('I read.')
 * Standard Estonian : luge-si-n ('I read.')
 * South Estonian Räpina dialects : lo-ì- ('I read.')
 * Livonian dialects : lug-ìZ- ('I read.')

The first person of plural
 * Standard Finnish : lu-i-mme ('We read.')
 * Finnish dialects : -mmen, -mmon, -mma
 * Vesjegonski Karelian dialects : luv-i-mma ('We read.')
 * Vepsian dialects : lug-i-mai ('We read.')
 * Ingrian dialects : lu-i-man ('We read.')
 * Standard Estonian : luge-si-me ('We read.')
 * South Estonian Räpina dialects : lo-ì-me̮ʔ ('We read.')
 * Livonian dialects : lug-ìZ-mə̑ ('We read.')

The second person of singular
 * Standard Finnish : lu-i-t ('You read.')
 * Vesjegonski Karelian dialects : luv-i-t ('You read.')
 * Vepsian dialects : lug-i-d́ ('You read.')
 * Ingrian dialects : lu-i-D ('You read.')
 * Standard Estonian : luge-si-d ('You read.')
 * South Estonian Räpina dialects : lo-ì-t̀ ('You read.')
 * Livonian dialects : lug-ìZ-t ('You read.')

The second person of plural
 * Standard Finnish : lu-i-tte ('You read.')
 * Finnish dialects : -tten, -tton, -tta
 * Vesjegonski Karelian dialects : luv-i-tta ('You read.')
 * Vepsian dialects : lug-i-tai ('You read.')
 * Ingrian dialects : lu-i-tta ('You read.')
 * Standard Estonian : luge-si-te ('You read.')
 * South Estonian Räpina dialects : lo-i-tte̮ ('You read.')
 * Livonian dialects : lug-ìZ-t(ə̑) ('You read.')

The third person of singular
 * Standard Finnish : luk-i ('She read.')
 * Vesjegonski Karelian dialects : lug-i ('She read.')
 * Vepsian dialects : lugo-b ('She read.')
 * Ingrian dialects : luG-i- ('She read.')
 * Standard Estonian : luge-s- ('She read.')
 * South Estonian Räpina dialects : luG-ì ('She read.')
 * Livonian dialects : lug-ìZ- ('She read.')

The third person of plural
 * Standard Finnish : luki-vat ('They read.')
 * Karelian dialects use indefinite voice instead : lugie-tti̮h ('They read.').
 * Vepsian dialects : lug-i-ba ('They read.')
 * Ingrian dialects : lukk-īD ('They read.') due to the consonant gradation in suffixes
 * Standard Estonian : luge-si-d ('They read.')
 * South Estonian Räpina dialects : lo-ì-vaʔ ('They read.')
 * Livonian dialects : lug-ìZ-t(ə̑) ('They read.')

title: Votian/Imperfect Tense


text:
User:GatorEngineer13245

All assignments due at 5:00PM EST on the due date.

 Homework Set 1: (due Sept. 9) ---> (UPDATE - due Sept. 16th) Covers lectures from Aug. 24 through Sept. 4

Problem 1: (Lecture 2-2, refers to 1-2)

Given a function $$f\left(y^1(t),t\right)$$, show that:

$$\frac{df}{dt}=\frac{\partial f}{\partial s}\dot{y}^1(t)+\frac{\partial f}{\partial t}$$

and

$$\frac{d^2f}{dt^2}=\frac{\partial f}{\partial s}\ddot{y}^1+\frac{\partial^2 f}{\partial^2 s}(\dot{y}^1)^2+2\frac{\partial^2 f}{\partial s \partial t}\dot{y}^1+\frac{\partial^2 f}{\partial^2 t}$$

Solution: Using the chain rule and the simplifying assumption that dy1=ds

$$\frac{df}{dt}=\frac{\partial f}{\partial s}\frac{\partial s}{\partial t}+\frac{\partial f}{\partial t}$$

ds/dt simplifies to $$\dot{y}^1$$ as shown

$$\frac{df}{dt}=\frac{\partial f}{\partial s}\dot{y}^1+\frac{\partial f}{\partial t}$$

For the second part we can write

$$\frac{d^2f}{dt^2}=\frac{d}{dt}\left ( \frac{df}{dt} \right )=\frac{d}{dt}\left (\frac{\partial f}{\partial s}\frac{\partial s}{\partial t}+\frac{\partial f}{\partial t} \right )$$

Using the product rule, this becomes:

$$\frac{d}{dt}\left (\frac{\partial f}{\partial s}\frac{\partial s}{\partial t}+\frac{\partial f}{\partial t} \right )=\frac{\partial s}{\partial t}\cdot \frac{d}{dt}\left (  \frac{\partial f}{\partial s} \right )+\frac{\partial f}{\partial s}\cdot \frac{d}{dt}\left ( \frac{\partial s}{\partial t} \right )+\frac{\partial^2 f}{\partial s \partial t}\cdot \frac{\partial s}{\partial t}+\frac{\partial^2 f}{\partial^2 t}$$

Completing the derivatives yields:

$$\frac{\partial s}{\partial t}\cdot \left ( \frac{\partial^2 f}{\partial^2 s}\cdot \frac{\partial s}{\partial t}+\frac{\partial^2 f}{\partial t \partial s} \right )+\frac{\partial f}{\partial s}\cdot \left ( \frac{\partial^2 s}{\partial^2 t} \right )+\frac{\partial^2 f}{\partial s \partial t}\cdot \frac{\partial s}{\partial t}+\frac{\partial^2 f}{\partial^2 t}$$

Again, substituting $$\dot{y}^1$$ for ds/dt and simplifying the expression yields

$$\frac{\partial^2 f}{\partial s^2}\left ( \dot{y}^1 \right )^2+2\cdot \frac{\partial^2 f}{\partial s \partial t}\dot{y}^1+\frac{\partial f}{\partial s}\ddot{y}^1+\frac{\partial^2 f}{\partial^2 t}$$

Problem 2: (Lecture 4-2)

Show that the solution of $$p^{\prime}+p=x$$ is $$p(x)=Ae^{-x}+x-1$$ using integrating factors. Problem 3: (Lecture 4-3)

Show that the first order ODE $$(2x^2+\sqrt{y})+x^5y^3y^{\prime}=0$$ is nonlinear

Solution A linear operator $$L\left ( \cdot \right )$$ is defined such that $$\forall\alpha,\beta \in\mathbb{R}$$, $$L(\alpha u+\beta v)=\alpha L(u)+\beta L(v)$$ Therefore, for $$F(x,y)=(2x^2+\sqrt{y})+x^5y^3y^{\prime}=0$$ to be linear Problem 4: (Lecture 5-2)

Given a function $$F(x,y,y^{\prime})=x^2y^5+6(y^{\prime})^2=0$$, show that F is a nonlinear 1st Order ODE. In other words, F does not satisfy the linearity condition $$\forall\alpha,\beta \in\mathbb{R}$$, $$F(\alpha u+\beta v)=\alpha F(u)+\beta F(v)$$ Problem 5: (Lecture 6-1)

Create an exact linear 1st Order ODE of the form $$\Phi_x(x,y)+\Phi_y(x,y)y^{\prime}=0$$ using the equation $$\Phi(x,y)=6x^4+2y^{3/2}$$ Create three more exact linear 1st Order ODEs by inventing new $$\Phi(x,y)$$ functions. Homework Set 2: (due Sept. 23) Covers lectures from Sept. 7 through Sept. 18 (not yet a complete listing)

Problem 1: (Lecture 7-1)

Given $$h_xN-h_yM+h(N_x-M_y)=0$$, solve for h(x,y) given that $$h_xN=0$$ Problem 2: (Lecture 8-2)

Given the Non-homogeneous Linear 1st Order ODE with Varying Coefficients $$y^{\prime}+\frac{1}{x}y=x^2$$, verify that the integrating factor necessary to make the ODE exact is $$h(x)=x$$ Problem 3: (Lecture 9-2)

Show that the Linear 1st Order ODE-VC $$\frac{1}{2}x^2y^{\prime}+[x^4y+10]=0$$ is exact Problem 4: (Lecture 9-3)

Show that $$\frac{1}{3}x^3(y^4)y^{\prime}+(5x^3+2)(\frac{1}{5}y^5)=0$$ is an exact nonlinear 1st Order ODE

Problem 5: (Lecture 10-3)

Determine if the 2nd condition for exactness is satisfied for $$(xy)y{}''+x(y{}'^{2})+yy{}'=0$$

title: User:GatorEngineer13245


text:
User talk:Nschiffer

 Hello Nschiffer, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Nschiffer


text:
User:Jay111

Hi there,

My name is Jay and I am currently studying screenwriting in London. I am interested in the whole of the cinematic production process and hope to learn a lot from this enlightening film making course.

title: User:Jay111


text:
User:Egm6321.f09.team7.hua

Hello, this is Brandon Hua. I== HW4: Problem 3 ==

Problem Statement and Given:  $$ xy''+2y'+xy=0$$ $$u_1(x)=\frac{sin(x)}{x}$$ Find $$u_2(x)$$ the second homogeneous solution

Solution: $$ xy''+2y'+xy=0$$ Divide by x to show general solution of: $$ y''+a_1y'+a_0y=0$$ $$ y''+\frac{2}{x}y'+1y=0$$ So: $$ a_1=\frac{2}{x}$$ $$ a_0=1$$

$$u_2=u_1(x)\int_{}^x \frac{1}{u_1^2(t)}e^{-\int_{}^t a_1(s)ds}dt$$ $$-\int_{}^t \frac{2}{s}ds=-2ln(t)=ln{\frac{1}{t^2}}$$ $$u_2=\frac{sin(x)}{x}\int_{}^x \frac{1}{\frac{sin^2(t)}{t^2}}e^{ln{\frac{1}{t^2}}}dt$$ $$u_2=\frac{sin(x)}{x}\int_{}^x \frac{sin^2(t)}{t^2}t^2dt$$ $$u_2=\frac{sin(x)}{x}\int_{}^x sin^2(t)dt$$ $$u_2=-\frac{sin(x)}{x}cot(x)$$ recall $$cot(x)=\frac{sin(x)}{cos(x)}$$ $$u_2=-\frac{cos(x)}{x}$$ Egm6321.f09.team7.hua 21:27, 21 October 2009 (UTC)

title: User:Egm6321.f09.team7.hua


text:
User talk:Egm6321.f09.Team 2.walker

 Hello Egm6321.f09.Team 2.walker, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Egm6321.f09.Team 2.walker


text:
User talk:Egm6321.f09.team7.hua

 Hello Egm6321.f09.team7.hua, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --mikeu talk 18:19, 13 September 2009 (UTC)

title: User talk:Egm6321.f09.team7.hua


text:
User talk:Jay111

 Hello Jay111, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --mikeu talk 18:19, 13 September 2009 (UTC)

title: User talk:Jay111


text:
User talk:GatorEngineer13245

 Hello GatorEngineer13245, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:GatorEngineer13245


text:
User talk:Egm6321.f09.team5.GV

 Hello Egm6321.f09.team5.GV, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Egm6321.f09.team5.GV


text:
User talk:Febby~enwikiversity

 Hello Febby, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Febby. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Febby~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:36, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:08, 19 April 2015 (UTC)

title: User talk:Febby~enwikiversity


text:
User talk:KaseyGalash

Hello Former Student!

I'm writing to you because you took a class from me in the past few years at the Art Institute. As of Spring, 2010, I'll not be teaching further classes at AIS for the foreseeable future. (We're parting ways on good terms!) Until now, you've been able to reach my Wikiversity educational resources from my website, but I've decided to delete that link. You can still reach all of those materials here.

If you're interested in what I'm up to in the future (which will include an album in 2010 and a novel in 2011) you can friend my facebook page or drop me an email at info@stevenarntson.info and you'll receive a periodic update about performances, classes, and publications.

If you know any current or former students of mine who might be interested in any of this, please forward this information if you have a moment.

I hope all is well for you.
 * Best! Stevenarntson

 Hello KaseyGalash, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:KaseyGalash


text:
User talk:Nulldev13

 Hello Nulldev13, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Nulldev13


text: Category:Search engines

title: Category:Search engines