J Janová
email: janova@physics.muni.cz

J Musilová

Nonholonomic mechanics: A geometrical treatment of general coupled rolling motion

In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a general coupled rolling motion. Two goals are stressed.

The first of them lies in the solution of an originally formulated problem of rolling motion of two rigid cylindrical bodies in the homogeneous gravitational field leading typically to nonlinear equations of motion. A solid cylinder can roll inside a ring under the static frictional force assuring rolling without slipping, the ring rolls again without slipping along a generally shaped terrain formed by hills and valleys. "Surprising behaviour" of the mechanical system which permits interesting applications is studied and discussed.

The second purpose of the paper is to show that the geometrical theory of nonholonomic constrained systems on fibered manifolds proposed and developed in the last decade by Krupková and others is an effective tool for solving nonholonomic mechanical problems. A comparison of this method to alternative methods is given and the benefits of coordinate-free formulation are mentioned.

In this paper, the geometrical theory is applied to the above mentioned mechanical problem. Both types of equations of motion resulting from the theory -deformed equations with the so called Chetaev type constraint forces containing Lagrange multipliers, and reduced equations free from multipliers -are found and discussed. Numerical solutions for two particular cases of the motion of the cylindrical system along a cylindrical surface are presented.

Introduction

The motion of mechanical systems is frequently subjected to various constraint conditions, holonomic or nonholonomic. Nonholonomic constraints lead typically to non-linear equations of motion of constrained system. While theories of holonomic or some special types of linear nonholonomic constraints are already well elaborated for quite general situations (see e.g. [START_REF] Brdička | Theoretical Mechanics (Teoretická mechanika[END_REF]), various theoretical approaches to general nonholonomic mechanics occur up to now, from the physical point of view on the one hand, and from the geometrical point of view on the other. As for physical approach we can mention the problem on a rotating table [START_REF] Ju | Dynamics of Nonholonomic Systems[END_REF], [START_REF] Swaczyna | Variational aspects of non-holonomic mechanical systems[END_REF] the pursuit problem e.g. in [START_REF] Janová | Geometrická teorie mechanických soustav s neholonomními vazbami (Geometrical theory of mechanical systems with nonholonomic constraints[END_REF] or [START_REF] Volný | Nonholonmic systems[END_REF], problem of knife in a paper e.g. in [START_REF] Ju | Dynamics of Nonholonomic Systems[END_REF], [START_REF] Volný | Nonholonmic systems[END_REF], or the problem of thin rolling disc on a horizontal plane in [START_REF] Brdička | Theoretical Mechanics (Teoretická mechanika[END_REF], [START_REF] Ju | Dynamics of Nonholonomic Systems[END_REF], [START_REF] Monforte | Geometric, Control and Numerical Aspects of Nonholonomic systems[END_REF] and recently in [START_REF] Batista | Steady motion of a rigid disc of finite thickness on horizontal plane[END_REF]. Various geometrical treatments can be found e.g. in [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF] - [START_REF] Sarlet | A geometrical framework for the study of nonholonomic Lagrangian systems II[END_REF] and many others.

On the other hand, in the last decade, and especially in last few years, alternative approaches were developed. In [START_REF] Udwadia | Equations of motion for mechanical systems: a unified approach[END_REF], a unified approach to mechanical systems with constraints non-linear in generalized velocities is given, leading to the Lagrange equations and the Gibbs-Appell equations. In [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF], a completely general approach to nonholonomic systems is presented for second order equations of motion, the constrained equations being given in the explicit form. The advantage of the method lies in the fact that it is not based on the principle of virtual work in its common sense, i.e., the constraints need not obey the d'Alembert's principle. Thus, the method admits a wide variety of constraint forces. Moreover in [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF], the authors formulate a generalized d'Alembert's principle. The theory is formulated exclusively in coordinates.

A geometrical derivation of Lagrange equations for a system of rigid bodies subject to general holonomic and nonholonomic constraints was given in [START_REF] Casey | Geometrical derivation of Lagrange's equations for a system of rigid bodies Math[END_REF]. There, the system is represented by an abstract particle P moving in a multidimensional Euclidean space, called Hertzian space,

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with the metric determined by the radius of gyration of the physical system. The holonomic constraints confine P to move in a Riemannian manifold (the configuration manifold of the constrained system) embedded in Hertzian space. Euler's laws for linear and angular momenta are expressed as a single balance equation in Hertzian space and Lagrange's equations emerge as covariant components of this equation taken along the coordinate directions in the configuration manifold. No appeal is made to variational principles or to notions of virtual work.

In [START_REF] Lauderdale | A method for relaxing parameter constraints in rigid body dynamics[END_REF], the theory of a pseudo-rigid body is used to establish equations of motion (free from parameter constraints) governing the motion of homogenously deforming body, which can be used to approximate the motion of a rigid body.

The geometrical theory used in the presented paper was presented for first order mechanical problems in [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF] and then generalized for higher order case in [START_REF] Krupková | Higher order mechanical systems with constraints[END_REF] brings an appropriate tool for constructing certain type of equations of motion of nonholonomic mechanical systems subjected to quite general constraints (an application to typically non-linear constraint see in [START_REF] Krupková | The relativistic particle as a mechanical system with nonlinear constraints[END_REF]). Let us give in this introductory section only a brief commentary to main ideas of the theory (for more details see Sec. 2) and its comparison with the above mentioned approaches [START_REF] Udwadia | Equations of motion for mechanical systems: a unified approach[END_REF], [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF], [START_REF] Casey | Geometrical derivation of Lagrange's equations for a system of rigid bodies Math[END_REF] and [START_REF] Lauderdale | A method for relaxing parameter constraints in rigid body dynamics[END_REF].

The theory is developed on fibered manifolds and their jet prolongations as underlying geometrical structures, naturally related to the character of physical problems. The main physical idea of the theory is based on the concept of Chetaev-type constraint forces introduced in analogy to "classical" Chetaev forces (see [START_REF] Chetaev | On the Gauss principle (in Russian)[END_REF]). Equations of corresponding unconstrained motion are connected with so called dynamical form and they define the components of this form. Using equations of constraints a special canonical distribution on first jet prolongation of the underlying manifold (corresponds to the phase space) can be constructed. Then first prolongations of admissible trajectories of the constrained motion are just integral sections of this distribution. By adding Chetaev-type forces (with Lagrange multipliers) to equations of motion, a dynamical form of the constrained problem is obtained and deformed equations of motion are constructed. These equations together with constraint conditions give the system of differential equations for unknown constrained trajectories and Lagrange multipliers. Another possible approach to the problem within the same theory starts from its description by so called Lepage class of forms instead the dynamical form itself. The Lepage class is, of course, closely related to the dynamical form, and it is obtained by the factorization of modules of forms by special submodules irrelevant from the point of view of the problem. This procedure leads to so called reduced equations of motion containing no Lagrange multipliers and giving the system of differential equations for constrained trajectories only. Nevertheless, constraint forces can be then obtained from deformed equations.

Note that the geometrical theory is effective not only for a wide class of "true" non-holonomic problems with non-linear or linear non-integrable constraints (such a problem cannot be solved by classical methods), but it can be directly applied to semiholonomic (integrable) constraints without the necessity to find the corresponding integrated constraint (which could require tedious technical calculations).

The method that we use, as well as that given in [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF], admits quite general nonholonomic constraints. On the other hand, our geometrical description of the situation with such completely general constraints is based, compared with [START_REF] Udwadia | Equations of motion for mechanical systems: a unified approach[END_REF] and [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF], on to some extent specific choice of constraint forces assuring the motion with desired constraints -the Chetaev-type forces. However, they represent a satisfactorily wide variety of constraint forces as for the possibility to obtain the description of a nonholonomic system realistic from the physical point of view, as shown e.g. in [START_REF] Krupková | The relativistic particle as a mechanical system with nonlinear constraints[END_REF] or [START_REF] Czudková | Non-holonomic mechanical systems and variational principle[END_REF], and they represent a generalization of d'Alembert's principle for constraints depending on velocities. Being geometrical, i.e. coordinate free, the method used in our paper gives a good understanding of geometrical structures naturally connected with nonholonomic constrained systems in general. Thus it can be used not only for second order mechanics, but it allows the immediate extension to higher order mechanics or field theory, taking into account higher jet prolongations of the underlying fibered manifold with the one-

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dimensional or multidimensional base, respectively. Such generalization is presented e.g. in [START_REF] Krupková | Higher order mechanical systems with constraints[END_REF] for higher order mechanics and in [START_REF] Krupková | Partial differential equations with differential constraints[END_REF] (general theory), [START_REF] Czudková | Non-holonomic constraint forces in field theory (geometrical theory applied)[END_REF] (a practical example) and [START_REF] Vankerschaver | Geometric aspects of nonholonomic field theories[END_REF] (theory and application) for the field theory. The method is also applicable to an arbitrary nonholonomic system of particles (mechanics) or continuum (field theory), including a system of rigid bodies such as studied in [START_REF] Casey | Geometrical derivation of Lagrange's equations for a system of rigid bodies Math[END_REF] and [START_REF] Lauderdale | A method for relaxing parameter constraints in rigid body dynamics[END_REF]. In addition, on the base of the geometrical theory with Chetaev-type constraint forces, one can formulate a constraint variational principle and solve the corresponding constraint inverse variational problem (see e.g. [START_REF] Krupková | Non-holonomic variational systems[END_REF]), as well as study symmetries of constrained systems. Symmetries and arising first integrals may then essentially simplify integration of the resulting constrained equations of motion, see e.g. [START_REF] Swaczyna | Variational aspects of non-holonomic mechanical systems[END_REF].(Nevertheless, in the present paper no attention is paid to higher order theories, field theories and the constraint variational problem.) Of course, the calculation procedure itself is made in coordinates. Its practical advantage lies in the possibility to choose appropriate coordinates, and also in two equivalent alternatives of solving the problem. The first of them is based on the solution of reduced equations of motion free of Lagrange multipliers and additional computation of these multipliers and corresponding constraint forces from dynamical equations, or alternatively, the direct solution of dynamical equations containing Lagrange multipliers. The decision between these two procedures is influenced by the concrete physical problem.

We discuss the following case of rolling motion: A smaller solid cylinder is put inside a ring and it can roll there without slipping. The ring can roll, again without slipping, along a generally shaped terrain in homogeneous Earth field with intensity (or gravitational acceleration) g. Even though the corresponding constraint is semiholonomic and thus it could be in principle treated by classical methods of Lagrange multipliers (for details concerning the method in general see e.g. the classical textbook of analytical mechanics [START_REF] Brdička | Theoretical Mechanics (Teoretická mechanika[END_REF]), the direct application of the Krupková's geometrical theory is very effective in this situation. As observed by the authors in a simple illustrative experiment (see figure 1), the proposed mechanical system generates different types of complicated motion depending on initial conditions: when placed on a horizontal plane and caused to roll without slipping, it sometimes begins to oscillate, sometimes rolls unevenly, stops, and then starts rolling in the direction opposite to that associated with the original motion. Moreover in this paper, we study theoretically a more complicated situation, when the system is placed on generally shaped terrain.

The studied system can be used as a model case for simulating real rolling and oscillatory motions of parts of machines in engineering. Moreover, according to the nature of its motion the studied mechanical system can be declared as the system with "surprising behaviour", as e.g. that shown in [START_REF] Kane | Realistic mathematical modeling of the rattleback[END_REF]. Note that apart from other possibilities, such systems can be effectively used as instructive examples.

The mentioned example has not been solved up to now for a generally shaped terrain: rolling without slipping is usually studied for a single body on an inclined or horizontal plane. The model of two cylinders (outer one and inner one) on an inclined plane is mentioned but not

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solved in [START_REF] Ju | Dynamics of Nonholonomic Systems[END_REF]. The aim of this paper is to use the geometrical theory for obtaining non-linear equations of motion of the above exposed mechanical problem and find their solution in some particular cases. This is made in Sec. 3, where both respective sets of equations of motion (reduced and deformed) are derived and graphical outputs of numerical solution are presented, whereas in Sec. 2 a brief review of ideas and results of the geometrical theory is presented, as necessary for its practical use.

Geometrical theory of nonholonomic mechanical systems: Ideas and results

Let us briefly recall the main results of the geometrical theory of nonholonomic constrained mechanical systems presented in [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF], [START_REF] Krupková | On the geometry of non-holonomic mechanical systems[END_REF], [START_REF] Krupková | Recent results in the geometry of constrained systems[END_REF]. Some simple physical examples of using this theory can be found in [START_REF] Janová | Geometrická teorie mechanických soustav s neholonomními vazbami (Geometrical theory of mechanical systems with nonholonomic constraints[END_REF], [START_REF] Volný | Nonholonmic systems[END_REF] or [START_REF] Janová | Mechanika neholonomně vázaných systému (Mechanics of nonholonomic constrained systems[END_REF].

Geometrical structures for unconstrained mechanical systems

Throughout the paper the standard notation of geometrical objects is used. As an underlying geometrical structure a (m+ 1)-dimensional fibered manifold (Y, π, X) with the one-dimensional base X is considered, (t ∈ X being time in non-relativistic mechanics), m-dimensional fibers (configuration space), and its jet prolongations (J s Y, π s , X) with s = 1, 2 for typical physical cases (a fiber of J 1 Y over t ∈ X represents the phase space). We denote (V, Ψ), Ψ = (t, q σ ),

1 ≤ σ ≤ m, a fibered chart on Y , (U, φ), U = π(V ), φ = (t), the associated chart on X and (V s , Ψ s ), V s = π -1
s (U), Ψ s = (t, q σ , q σ s ) the associated fibered chart on J s Y , where q σ 1 = qσ and q σ 2 = qσ . Moreover, denote by π r,s :

J r Y → J s Y , 0 ≤ s < r ≤ 2, J 0 Y = Y , canonical projections. A section of fibered manifold (Y, π, X) is a smooth mapping γ : I → Y , such that γ • π = id I , I ⊂ X being an open set. Analogously sections of (J r Y, π r , X) are defined. A section δ of (J r Y, π r , X) is called holonomic if it is of the form δ = J r γ,
where γ is a section of (Y, π, X).

Recall that a vector field ξ on J r Y is called π r -projectable if there exists a vector field ξ 0 on X such that T π r ξ = ξ 0 • π r . A vector field ξ is called π r -vertical if T π r ξ = 0. A form η on J r Y is called π r -horizontal if its contraction by an arbitrary chosen π r -vertical vector field ξ vanishes, i.e. it holds i ξ η = 0. A form η is called contact if J r γ * η = 0 for all sections γ of (Y, π, X). Concepts of π r,s -projectable vector field, π r,s -vertical vector field, and π r,s -horizontal form are defined by the quite analogous way. Moreover, for every k-form η on J r Y there exists the unique decomposition into its q-contact components, 0 ≤ q ≤ k, π * r+1,r η = k q=0 p q η, the 0-contact component p 0 η = hη is called also the horizontal one.

From the point of view of physics, all possible trajectories of a so-called first order unconstrained mechanical system on a fibered manifold are given just by sections γ of (Y, π, X) such that they are solutions of the system of m second order ordinary differential equations of motion (affine in accelerations),

E σ • J 2 γ = 0, E σ = A σ (t, q λ , qλ ) + B σν (t, q λ , qλ )q ν , ( 1
)
where 1 ≤ λ ≤ m and Einstein summation is used. Consider the 1-contact π 2,0 -horizontal 2-form on J 2 Y , E = E σ ω σ ∧ dt, called dynamical form. A solution γ of equations ( 1) is called a path of E. We define the Lepage class [α] of E by the requirement p 1 α = E (see [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF] or [START_REF] Krupková | The Geometry of Ordinary Variational Equations[END_REF]). The class [α] is called also the mechanical system. Every representative of this class is of the form

α = A σ ω σ ∧ dt + B σν ω σ ∧ d qν + F σν ω σ ∧ ω ν ,
where ω σ = dq σqσ dt are contact 1-forms forming the basis of 1-forms (dt, ω σ , qσ ) on J 1 Y adapted to the contact structure. So, [α] = α mod 2-contact forms. The following proposition was proved (see [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF] or [START_REF] Krupková | The Geometry of Ordinary Variational Equations[END_REF]):

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A section γ of (Y, π, X) is a path of the dynamical form E if and only if

J 1 γ * i ξ α = 0. ( 2
)
for every π 1 -vertical vector field ξ on J 1 Y .

Geometry of nonholonomic constrained systems

A nonholonomic constrained mechanical system is defined on the (2m + 1k)-dimensional constraint submanifold Q ⊂ J 1 Y fibered over Y and given by k equations (1 ≤ k ≤ m -1)

f i (t, q σ , qσ ) = 0, such that rank ∂f i ∂ qσ = k, 1 ≤ i ≤ k, or in the explicit normal form qm-k+i -g i (t, q σ , ql ), 1 ≤ l ≤ m -k. ( 3
)
It is evident that only admissible trajectories of a nonholonomic mechanical system are such sections γ :

I t → Y for which J 1 γ(t) ∈ Q for all t ∈ I, i.e. f i • J 1 γ = 0 for 1 ≤ i ≤ k (so-called Q-admissible sections).
The constraint (3) gives rise to the canonical distribution C of codimension k on Q. Its annihilator is of the form

C 0 = span{ϕ i }, ϕ i = - ∂g i ∂ ql ω l + ι * ω m-k+i , ( 4
)
where ι : Q → J 1 Y is the canonical embedding. The canonical distribution is closely related to the constraint ideal I(C 0 )

I(C 0 ) = {ϕ i ∧ χ i |χ i is a form on Q}, (5)
where ϕ i are 1-forms on Q called canonical constraint 1-forms. The importance of the canonical distribution is evident from its following property (see [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF], [START_REF] Swaczyna | Variational aspects of non-holonomic mechanical systems[END_REF]):

A section γ of Y is Q-admissible if and only if J 1 γ is an integral section of the canonical distribution.

We have already mentioned in Sec. 1 that there are two possible equivalent approaches to the description of non-holonomic mechanical systems -one of them, called physical, is based on deformed equations with constraint forces and Lagrange multipliers and the other, geometrical one, uses reduced equations.

Geometrical approach introduces the constrained mechanical system related to the mechanical system [α] by the equivalence relation

[α Q ] = [ι * α] mod I(C 0 ). (6)
A Q-admissible section γ of (Y, π, X) is called a path of the constrained system [α Q ] if for every π 1 -vertical vector field ξ belonging to the canonical distribution it holds

J 1 γ * i ξ α = 0. ( 7
)
The following proposition can be formulated (see again [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF]):

Proposition. A section γ of (Y, π, X) is a path of the deformed system [α Φ ] if and only if for every π 1 -vertical vector field ξ belonging to C holds

f i • J 1 γ = 0, Āl + Bls qs • J 2 γ = 0, ( 8
)
where

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Āl = A l + k j=1 A m-k+j ∂g j ∂ ql + k i=1 B l,m-k+i + k j=1 B m-k+j,m-k+i ∂g j ∂ ql • • ∂g i ∂t + ∂g i ∂q σ qσ • ι, (9)
Bls = B ls + k i=1 B l,m-k+i ∂g i ∂ qs + B m-k+i,s ∂g i ∂ ql + B m-k+j,m-k+i ∂g j ∂ ql ∂g i ∂ qs • ι . ( 10
)
Relations (8) represent the system of reduced equations for m unknown functions q σ γ (k of them are first order and (mk) second order ordinary differential equations).

Physical approach is based on Chetaev-type constraint forces. Such a force is given by the constraint itself, in analogy with holonomic situations. It is expressed by the dynamical form

Φ = Φ σ ω σ ∧ dt = μ i ∂f i ∂ qσ ω σ ∧ dt, 1 ≤ i ≤ k, ( 11
)
where functions μ i (t, q λ , qλ ) are Lagrange multipliers.

(Note that such a dynamical form satisfies the generalized principle of virtual work i ξ Φ| U = 0 for every π 1 -vertical vector field ξ belonging to the constraint distribution

C U , C 0 U = span{ϕ i , df i , 1 ≤ i ≤ k}, U, U ∩ Q = ∅ being an open set of a chart on J 1 Y , see [9].) Denote [α Φ ] = [α-Φ], α Φ = A σ -μ i ∂f i ∂ qσ ω σ ∧ dt+B σν ω σ ∧ d qν +F σν ω σ ∧ ω ν . ( 12
)
The equivalence class [α Φ ] is called the

deformed mechanical system. A Q-admissible section γ of (Y, π, X) is called a path of [α Φ ] if (E σ -Φ σ ) • J 2 γ.
The following proposition holds (see [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF], [START_REF] Krupková | On the geometry of non-holonomic mechanical systems[END_REF]):

Proposition. A section γ of Y is a path of the deformed system [α Φ ] if and only if for every π 1 -vertical vector field ξ on J 1 Y it holds

J 1 γ * i ξ α Φ = 0 or equivalently A σ +B σν qν = μ i ∂f i qσ , and f i • J 1 γ = 0 . ( 13
)
System ( 13) is given by k first order and m second order ordinary differential equations for unknown functions μ i and q σ γ and it represents the deformed equations.

Semiholonomic constraints:

Let us now describe a special type of nonholonomic constraints, called semiholonomic. Such conditions usually take place for rolling of rigid bodies without slipping. A system of constraints ( 3) is called semiholonomic if the constraint ideal ( 5) is differential, i.e. the canonical distribution ( 4) is completely integrable (see e.g. [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF]). This means that dϕ ∈ I(C 0 ) and thus following conditions hold

∂ c g i ∂q l - d c dt ∂g i ∂ ql = 0, ∂ 2 g i ∂ qs ∂ ql = 0, 1 ≤ l, s ≤ m -k, 1 ≤ i ≤ k, ( 14
)
where

∂ c ∂q l = ∂ ∂q l + ∂g j ∂ ql ∂ ∂q m-k+j , d c dt = ∂ ∂t + ql ∂ ∂q l + g j ∂ ∂q m-k+j .

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In the following section we apply the obtained equations ( 8) and ( 13) obtained for general nonholonomic mechanical system to the example of two rolling cylinders mentioned in Sec. 1. Let < O; x, y, z > be a fixed cartesian system of coordinates with z-axis directed vertically upward (oppositely to gravitational acceleration g). Let V be a very thin ring of radius R and mass M. It can roll on the terrain without slipping.

General coupled rolling of ring and cylinder

The mechanical model

Suppose that the terrain is generally shaped by a function z(x), i.e. it is formed by hills and valleys in < O; x, z >. Thus, the ring moves by such a way that it touches the terrain in the surface line parallel to the y-axis. Denote as ϕ the angle formed by the coordinate plane < O; x, y > and the plane tangent to both the terrain and the ring surface at the line of contact. Thus ϕ can be in principle considered as a known function of X and Z coordinates of centre of mass of the ring V.

A solid cylinder W of mass m and radius r, r < R, is placed to V and it can roll inside without slipping (see figure 2).

The momenta of inertia of cylinders V and W with respect to their symmetry axes in both cases are J M = MR 2 and J m = 1/2mr 2 , respectively. Moreover, let us suppose that none of the cylinders can move along the y-axis and thus the y-coordinates of their centres of mass are constant.

Unconstrained mechanical system

Using the geometrical theory of nonholonomic system mentioned in Sec. 2 we define the structure of mechanical system as follows:

There are six degrees of freedom of the corresponding unconstrained mechanical system, i.e. m = 6. Thus, the fibered manifold of the problem is (R × R 6 , pr 1 , R), where pr 1 is the cartesian projection on the first factor.

We choose the fibered chart on Y as (V, Ψ), where V is an open set V ⊂ Y and Ψ = (t, q 1 , q 2 , q 3 , q 4 , q 5 , q 6 ) = ( t,ψ,β,x,z,X,Z). The associated chart on the base is (pr 1 , Φ), Φ = (t), where t is the time coordinate, and associated fibered chart on ψ,β,x,z,X,Z,ψ,β,ẋ,ż,Ẋ,Ż). Coordinates (X, Z) and (x, z) define the position of center of mass of V and W in < O; x, z >plane, respectively. The variables β and ψ represent angles of rotation of V and W, respectively (see figure 3).

J 1 Y = R × R 6 × R 6 is (V 1 , Ψ 1 ), V 1 = pr -1 (V ), Ψ 1 ), Ψ 1 = (t, q σ , qσ ), 1 ≤ σ ≤ 6, i.e. Ψ 1 = (t,
The Lagrange function of unconstrained mechanical system is given by

L = 1 2 m( ẋ2 + ż2 ) + 1 2 M( Ẋ2 + Ż2 ) + 1 2 J m ψ2 + 1 2 J M β2 -mgz -MgZ.

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Figure 3: The scheme of the the ring and the cylinder

x z ϕ v V ψ β R r
Then the corresponding Euler-Lagrange equations of motion ( 1) are

E 1 ≡ -J m ψ = 0, E 2 ≡ -J M β = 0, E 3 ≡ -mẍ = 0, E 4 ≡ -mz -mg = 0, E 5 ≡ -M Ẍ = 0, E 6 ≡ -M Z -Mg = 0.
The Lepage class of the unconstrained mechanical system is thus given by the representative

α = -mgω 4 ∧ dt -Mgω 6 ∧ dt -J m ω 1 ∧ d ψ -J M ω 2 ∧ d β - -m(ω 3 ∧ d ẋ + ω 4 ∧ d ż) -M(ω 5 ∧ d Ẋ + ω 6 ∧ d Ż),
where ω 1 = dψ -ψdt, ω 2 = dβ -βdt, ω 3 = dxẋdt, ω 4 = dzżdt, ω 5 = dX -Ẋdt, ω 6 = dZ -Żdt.

The constraint

The nonholonomic constraint is given by conditions of rolling without slipping required for both bodies, the ring and the cylinder. The equations of the constraint are as follows:

ẋ ≡ g 1 = ẋ1 + R β cos ϕ, ( 15
) ż ≡ g 2 = ẏ1 + R β sin ϕ, ( 16
) Ẋ ≡ g 3 = R β cos ϕ, ( 17
) Ż ≡ g 4 = R β sin ϕ, ( 18
)
where v 1 = ( ẋ1 , 0, ż1 ) = ( ẋ -Ẋ, 0, ż -Ż) is the relative velocity of centers of mass (W with respect to V) and ϕ = ϕ(X, Z) is known function. Conditions ( 15) and ( 16) represent the fact that the cylinder W rolls without slipping inside the ring V, conditions [START_REF] Sarlet | A geometrical framework for the study of nonholonomic Lagrangian systems[END_REF] and [START_REF] Sarlet | A geometrical framework for the study of nonholonomic Lagrangian systems II[END_REF] ensure the rolling of the ring V on the terrain. The sense of second two conditions is immediately clear from two facts: the velocity V = ( Ẋ, 0, Ż) is parallel with the tangent plane to the terrain profile, and for rolling without slipping it holds V = R β, β being the angular speed of V. Let us perform a derivation of constraints ( 15) and ( 16) (see figure [START_REF] Janová | Geometrická teorie mechanických soustav s neholonomními vazbami (Geometrical theory of mechanical systems with nonholonomic constraints[END_REF]). The components of the relative velocity vector v 1 are

v 1 = ( ẋ1 , 0, ż1 ) = v 1 (cos χ, 0, sin χ),
where the speed v 1 is a function of ψ and β. The angle χ determines the location of the small cylinder on the interior face of the ring (see figure [START_REF] Janová | Geometrická teorie mechanických soustav s neholonomními vazbami (Geometrical theory of mechanical systems with nonholonomic constraints[END_REF]). The cylinder W rolls without slipping and thus it holds

v 1 = (R -r) χ, i.e. ẋ1 = (R -r) χ cos χ, ż1 = (R -r) χ sin χ. ( 19
)
Figure [START_REF] Janová | Geometrická teorie mechanických soustav s neholonomními vazbami (Geometrical theory of mechanical systems with nonholonomic constraints[END_REF] shows an additional angle δ, which determines a total rotation angle of the cylinder W with respect to the ring V. It holds

δ = ψ + χ, rδ = R(β + χ) and then χ = r R -r ψ - R R -r β. ( 20
)
Denoting

C = cos χ = cos r R -r ψ - R R -r β , S = sin χ = sin r R -r ψ - R R -r β . ( 21
)
and substituting χ given by [START_REF] Udwadia | On the foundations of analytical dynamics[END_REF] into equations [START_REF] Udwadia | Equations of motion for mechanical systems: a unified approach[END_REF] we have

ẋ1 = (r ψ -R β) C, ż1 = (r ψ -R β) S. (22)
Substituting ( 22) into ( 15) and ( 16) and adding conditions ( 17) and ( 18) we get the constraint equations in the form:

ẋ ≡ g 1 = (r ψ -R β) C + R β cos ϕ, ż ≡ g 2 = (r ψ -R β) S + R β sin ϕ, ( 23
) Ẋ ≡ g 3 = R β cos ϕ, Ż ≡ g 4 = R β sin ϕ.
These four nonholonomic conditions define the constraint submanifold Q of dimension dimQ = 9. The constraint [START_REF] Krupková | The relativistic particle as a mechanical system with nonlinear constraints[END_REF] obeys conditions [START_REF] Ch | Reduction of constrained mechanical systems and stability of relative equilibria[END_REF], i.e. it is semiholonomic. The geometric theory enables us to solve such a problem immediately, without integrating the constraint.

A c c e p t e d m

a n u s c r i p t

Constrained mechanical system -reduced equations

The geometrical approach described in Sec. 2, eqs. ( 8), ( 9), [START_REF] Krupková | Higher order mechanical systems with constraints[END_REF], applied to our problem leads to the constrained mechanical system [α Q ] related to the unconstrained mechanical system [α].

The class [α Q ] is generated e.g. by the following representative:

α Q = Ā1 ω 1 ∧ dt + Ā2 ω 2 ∧ dt + B11 ω 1 ∧ d ψ + B22 ω 2 ∧ d β + B12 ω 1 ∧ d β + B21 ω 2 ∧ d ψ, where Ā1 = -mgr S -mSrR 2 β2 cos ϕ ∂ϕ ∂X + sin ϕ ∂ϕ ∂Z , Ā2 = gR{m S -(M + m) sin ϕ} + + mSR (r ψ -R β) 2 R -r + R 2 β2 cos ϕ ∂ϕ ∂X + sin ϕ ∂ϕ ∂Z , B11 = -mr 2 -J m , B22 = -MR 2 -J M -2mR 2 (1 -C), ( 24
) B12 = B21 = mrR(1 -C),
and quantities C = cos χ, S = sin χ are given by relations [START_REF] Casey | Geometrical derivation of Lagrange's equations for a system of rigid bodies Math[END_REF], while C = cos (χ + ϕ), S = sin (χ + ϕ).

The reduced equations are of the form:

( Ā1 + B11 ψ + B12 β) • J 2 γ = 0, ( Ā2 + B22 β + B21 ψ) • J 2 γ = 0 ẋ -(r ψ -R β) C -R β cos ϕ = 0, (25)
ż

-(r ψ -R β) S -R β sin ϕ = 0, Ẋ -R β cos ϕ = 0, Ż -R β sin ϕ = 0.
There is no analytical solution of reduced equations of motion, in general situation.

Constrained mechanical system -deformed equations

Deformed equations are obtained by the physical approach described in Sec. 2 and based on Chetaev-type constraint forces. Such a force is in our case given by Φ = Φ 1 + Φ 2 + Φ 3 + Φ 4 , where

Φ 1 = μ 1 (-r C, R C -R cos ϕ, 1, 0, 0, 0), Φ 2 = μ 2 (-r S, R S -R sin ϕ, 0, 1, 0, 0), Φ 3 = μ 3 (0, -R cos ϕ, 0, 0, 1, 0), Φ 4 = μ 4 (0, -R sin ϕ, 0, 0, 0, 1).
Deformed equations of motion are:

-J m ψ + μ 1 r C + μ 2 r S = 0, -J M β -μ 1 R C -R cos ϕ - -μ 2 R S -R sin ϕ + μ 3 R cos ϕ + μ 4 R sin ϕ = 0, -mẍ -μ 1 = 0, -mz -mg -μ 2 = 0, ( 26
) -M Ẍ -μ 3 = 0, -M Z -Mg -μ 4 = 0.
(0) = 0 x(0) = √ 0.51(Q -R), z(0) = 0.7(R -Q) -(R -r), X(0) = √ 0.51(Q -R), Z(0) = 0.7(R -Q), ψ(0) = 0, β(0) = 0, ψ(0) = 0, β(0) = 0.
The first set of initial conditions means that at the time t = 0s the small cylinder W lies at the bottom of the ring V, and V lies at the bottom of the fixed ring and begins to move left. The second set corresponds to the fact that at the time t = 0s the small cylinder W lies at the bottom of the ring V, and V is sticked on the right side of the hollow and at the time t = 0s is unsticked.

Numerical solutions was made with help of the program Maple. The results for individual choices of initial conditions are presented in figures 5, 6, 7 and 8, 9, 10.

Conclusion

The mechanical problem of general coupled rolling of ring and cylinder itself enlarges the "reservoir" of solved non-linear mechanical problems. Moreover, the presented results show the effectiveness of the geometrical theory [START_REF] Krupková | Mechanical systems with nonholonomic constraints[END_REF] of nonholonomic constraints for formulating equations of motion of concrete nonholonomic mechanical systems with constraints based on the assumption of rolling without slipping. For semiholonomic (integrable) constraints an advantage of the theory lies also in the possibility to include the constraint directly into the equations of motion. Then it appears that the model of Chetaev-type forces is appropriate for describing the studied type of the constraint from the point of view of physics.

Figure 1 :

 1 Figure 1: Illustrative experiment

Figure 2 :

 2 Figure 2: The scheme of the problem

A c c e p t e d m a n u s c r i p t

Figure 4 :

 4 Figure 4: Specifying v 1

Figure 5 : 4 Figure 6 :

 546 Figure 5: Numerical solution for initial conditions (a), X(t) and x(t)

Figure 7 : 7 Figure 8 :Figure 9 :

 7789 Figure 7: Numerical solution for initial conditions (a), β(t) a ψ(t)

Figure 10 :

 10 Figure 10: Numerical solution for initial conditions (b), β(t) a ψ(t)

A c c e p t e d m a n u s c r i p t A c c e p t e d m a n u s c r i p t

Acknowledgements

The research is supported by the grant 201/06/0922 of the Czech Grant Agency and by the grant MSM0021622409 of the Ministry of Education, Youth and Sports of the Czech Republic.

The authors are indebted to Dr. Lenka Czudkova for discussions and comments to the Sec.1 and Sec.2.

A c c e p t e d m a n u s c r i p t

From the physical point of view it is evident that Chetaev forces would have the character of normal stress forces and statical frictional forces. Let us write down Newton equations of motion for completeness.

Let us denote N = (N x , N y , N z ) and -N = (-N x , -N y , -N z ) the sum of statical frictional and stress forces acting in the contact point on cylinder W and V, respectively. Let P = (P x , P y , P z ) is the sum of stress and statical frictional forces of the terrain acting on V.

We require N y = 0, P y = 0. Let us denote M W the torque of the force N with respect to center of mass of W and M V1 and M V2 torques of forces -N and P , respectively, with respect to center of mass of V. Denoting r = r( S, 0, -C), R 2 = R(sin ϕ, 0,cos ϕ) we have

Taking into account that Y = y = const, we obtain corresponding Newton equations:

The constraint conditions are the same as in Sec. 3.3, i.e. ( 15), ( 16), ( 17), [START_REF] Sarlet | A geometrical framework for the study of nonholonomic Lagrangian systems II[END_REF]. Comparing the obtained Newton equations with the system of deformed equations of motion [START_REF] Krupková | Partial differential equations with differential constraints[END_REF] we can see that μ 1 = -N x , μ 2 = -N z , μ 3 = N x -P x , μ 4 = N z -P z . Hence Chetaev constraint force has the meaning of the generalized physical forces (i.e. forces and torques).

Numerical solution of reduced equations of motion

Suppose that the terrain profile is cylindrical, i.e. the body V can roll inside a grater fixed ring with radius Q. The axes of all cylinders are parallel. Let the axis of the fixed cylinder go through coordinate origin. Then it holds

In such a case the reduced equations take the form [START_REF] Czudková | Non-holonomic mechanical systems and variational principle[END_REF] with

Quantities C = cos χ, S = sin χ are again given by relations [START_REF] Casey | Geometrical derivation of Lagrange's equations for a system of rigid bodies Math[END_REF], and C = cos (χ + ϕ), S = sin (χ + ϕ), The numerical solution of reduced equations was made under following conditions:

Parameters of the mechanical system: M = 1.0kg, m = 0.1kg, R = 1.0m, r = 0.6m, Q = 6.0m.

Two cases of initial conditions (lengths in meters, time in seconds):

(a) x(0) = 0, z(0) = -Q + r, X(0) = 0, Z(0) = -Q + R, ψ(0) = 0, β(0) = 0, ψ(0) = 0, β(0) = -0.35,


S Sánchez

R Martínez

A García

D Vidal

J E Blanco

M Blanco

A Mora

S Herrera-León

A Echeita

J M Alonso

J Rey

Detection and characterisation of O157:H7 and non-O157 Shiga toxin-producing Escherichia coli in wild

Keywords: Shiga toxin-producing Escherichia coli (STEC), E. coli O157:H7, Wild boars, Serotyping, Phage typing, Pulsed-field gel electrophoresis

published or not. The documents may come   L'archive ouverte pluridisciplinaire

A c c e p t e d M a n u s c r i p t

Introduction

Shiga toxin-producing Escherichia coli (STEC) have recently emerged as important food-borne pathogens, especially serotype O157:H7. Human diseases ranging from mild diarrhoea to haemorrhagic colitis and haemolytic uraemic syndrome (HUS) can be caused by STEC, typically affecting children, the elderly, and immunocompromised patients (Centers for Disease [START_REF] Centers For | Outbreaks of Escherichia coli O157:H7 infections among children associated with farm visits -Pennsylvania and Washington, 2000[END_REF]. The pathogenic capacity of STEC resides in a number of virulence factors, including Shiga toxins (Stx1 and Stx2), intimin, enterohaemolysin, and the STEC autoagglutinating adhesin (Saa) [START_REF] Gyles | Shiga toxin-producing Escherichia coli: an overview[END_REF].

Healthy domestic ruminants such as cattle, sheep, and goats can harbour STEC and E. coli O157:H7 in their faeces and are thus natural reservoirs of these pathogens (Blanco et al., 2004b;[START_REF] Orden | A longitudinal study of verotoxin-producing Escherichia coli in two dairy goat herds[END_REF]Sánchez et al., 2009b).

However, E. coli O157:H7 and non-O157 STEC strains have also been isolated from wild ruminants [START_REF] Renter | Escherichia coli O157:H7 in free-ranging deer in Nebraska[END_REF][START_REF] García-Sánchez | Presence of Shiga toxin-producing E. coli O157:H7 in a survey of wild artiodactyls[END_REF]Sánchez et al., 2009a), and deer have been implicated in the food-borne transmission of E. coli O157:H7 to humans in Japan [START_REF] Nagano | Phenotypic and genotypic characterization of β-D-glucuronidase-positive Shiga toxin-producing Escherichia coli O157:H7 isolates from deer[END_REF] and in the United States [START_REF] Keene | An outbreak of Escherichia coli O157:H7 infections traced to jerky made from deer meat[END_REF][START_REF] Rabatsky-Ehr | Deer meat as the source for a sporadic case of Escherichia coli O157:H7 infection, Connecticut[END_REF]. Recent experimental and epidemiologic studies suggest that domestic pigs are biologically competent hosts and a potential reservoir of E. coli O157:H7 [START_REF] Feder | Isolation of Escherichia coli O157:H7 from intact colon fecal samples of swine[END_REF][START_REF] Cornick | Transmission and infectious dose of Escherichia coli O157:H7 in swine[END_REF]. Actually, E. coli O157:H7 strains have been identified in wild boars in Sweden (Wahlström et al., 2003) and feral swine in the United States, where feral swine near spinach fields shed the outbreak strain in a nationwide spinach-associated outbreak of E. coli O157:H7 [START_REF] Jay | Escherichia coli O157:H7 in feral swine near spinach fields and cattle, central California coast[END_REF]. Nevertheless, there are no reports of the isolation of STEC other than E. coli O157:H7 from wild boars and, to our knowledge, the occurrence of E. coli O157:H7 and non-A c c e p t e d M a n u s c r i p t 4 O157 STEC in wild boars in Spain is not known. The objectives of this study were to establish the prevalence of E. coli O157:H7 and non-O157 STEC in freeranging wild boars killed during the hunting season in southwest Spain and to characterise them, in order to determine if wild boars represent a potential risk to public health.

Materials and methods

Sample collection, culture, and STEC screening

During the 2007-2008 hunting season (from mid-October to mid-February), a total of 212 European wild boars (Sus scrofa) killed by hunters in different game estates in the Extremadura region in southwest Spain were sampled. On each sampling occasion, one sample of rectal faeces per animal was collected from harvested individuals. Samples were transported to the laboratory under refrigeration in Cary-Blair transport medium (Deltalab, Barcelona, Spain) and placed in culture media within 24 h of collection.

For isolation of non-O157 STEC, faecal samples were plated directly onto MacConkey agar (Oxoid, Basingstoke, England). Following overnight incubation, 10 suspect E. coli colonies were tested for the genes encoding Stx1 and Stx2 toxins (stx 1 and stx 2 genes) by PCR as previously described [START_REF] Rey | Serotypes, phage types and virulence genes of Shigaproducing Escherichia coli isolated from sheep in Spain[END_REF]. The resulting STEC isolates were confirmed biochemically as E. coli by the API 20E system (bioMérieux, Marcy L'Etoile, France) and tested for the genes encoding intimin (eae gene), enterohaemolysin (ehxA gene), and Saa (saa gene) as previously described (Sánchez et al., 2009a). When isolates from a given sample exhibited similar genetic characteristics in terms of the presence or absence of virulence genes, only one colony was selected and stored at -80 ºC until further A c c e p t e d M a n u s c r i p t 5 characterisation. Otherwise, when isolates with different genetic characteristics were obtained, one colony of each was selected and stored for further characterisation. For isolation of E. coli O157:H7, faecal samples were examined by enrichment culture in modified buffered peptone water, concentration of E. coli O157 by immunomagnetic separation with Dynabeads anti-E. coli O157 (Dynal, Oslo, Norway), and culture of magnetic beads onto cefixime tellurite sorbitol MacConkey agar (Oxoid). Following overnight incubation, 10 nonsorbitol-fermenting colonies were tested for the genes encoding O157 and H7 antigens (O157 rfbE and fliCh7 genes) by PCR as previously described (García- [START_REF] García-Sánchez | Presence of Shiga toxin-producing E. coli O157:H7 in a survey of wild artiodactyls[END_REF]. The resulting E. coli O157:H7 isolates were confirmed biochemically as E. coli by the API 20E system (bioMérieux) and tested for the genes encoding Stx1 and Stx2 toxins, intimin (eae and eae-γ1 variant), and enterohaemolysin. β-glucuronidase (GUD) activity in E. coli O157:H7 isolates was investigated on Chromocult Coliform agar (Merck, Darmstadt, Germany) after overnight incubation. The eae type was determined for all eae-positive isolates as previously described [START_REF] Rey | Serotypes, phage types and virulence genes of Shigaproducing Escherichia coli isolated from sheep in Spain[END_REF].

Characterisation of isolates

The identification of O and H antigens in isolates was carried out as described by [START_REF] Guinée | Escherichia coli associated with neonatal diarrhoea in piglets and calves[END_REF] Pulsed-field gel electrophoresis (PFGE) was used to establish relatedness and diversity among E. coli O157:H7 isolates. PFGE was performed in accordance with the PulseNet-Europe protocol (http://www.pulsenet-europe.org/docs.htm).

Genomic DNA was digested with XbaI (Roche Diagnostics, Mannheim, Germany) and analyzed in 1% agarose gels (Bio-Rad, Hemel Hempstead, United Kingdom) in 0.5× TBE buffer at 14 ºC using the CHEF MAPPER system (Bio-Rad). The runtime was 21.3 h at 6 V/cm, with initial and final switch times of 2.16 and 54.17 s, respectively. The XbaI-digested DNA from Salmonella enterica Braenderup H9812 was used as a molecular size marker. Resultant images were analyzed with the InfoQuestFP software (Bio-Rad). Isolates were allocated a different PFGE type when a genetic difference could be detected. Cluster analysis was performed using the Dice coefficient and the unweighted pair group method with arithmetic averages (UPGMA).

Results and discussion

Overall, STEC were detected in 17 (8.0%) of the animals sampled. E. coli O157:H7 was isolated from 7 (3.3%) animals and non-O157 STEC were isolated from 11 (5.2%). Two different strains were identified in samples from 2 animals, in one of which both E. coli O157:H7 and non-O157 STEC (O6:H10) were isolated. These results indicate a high prevalence of STEC infection in freeranging wild boars in this area of Spain, with a higher prevalence rate of E. coli A c c e p t e d M a n u s c r i p t 7 O157:H7 (3.3%) than in a previous study in Sweden (1.5%) (Wahlström et al., 2003).

All isolates obtained in the present study (19 in total) were further characterised (Table 1 The PCR procedure indicated that 4 isolates carried the stx 1 gene, 12 carried the stx 2 gene, and 1 contained both of these genes. The ehxA, eae, and saa genes were detected in 13, 8, and 1 of the isolates, respectively. The 8 eae-positive isolates comprised the types eae-γ1 (7 isolates) and eae-δ (1 isolate), which are intimin subtypes previously reported within ovine, bovine, and human STEC strains [START_REF] Rey | Serotypes, phage types and virulence genes of Shigaproducing Escherichia coli isolated from sheep in Spain[END_REF]Blanco et al., 2004a;Blanco et al., 2004b). There were 12 different associations between serotype and virulence genes among the 19 isolates, being O157:H7 stx 2 eae-γ1 ehxA the most commonly found association (5 isolates), followed by O157:H7 eae-γ1 ehxA, O157:H21 stx 2 ehxA, and O23:H21 stx 2 (2 isolates each). Two isolates among the 7 E. coli O157:H7 isolates were stxnegative, although they carried genes encoding other virulence-associated factors (intimin and enterohaemolysin). Whether this finding resulted from the loss of stx gene(s) from initially stx-positive strains remains unclear. However, whilst the human health risks associated with stx-negative E. coli O157:H7 strains may be less significant, the acquisition of stx-carrying phages from the environment cannot be excluded [START_REF] Muniesa | Comparative survival of free Shiga toxin 2-encoding phages and Escherichia coli strains outside the gut[END_REF].

A c c e p t e d M a n u s c r i p t

8

The E. coli O157:H7 isolates neither fermented sorbitol nor exhibited GUD activity after overnight incubation. Two isolates expressed the H7 antigen and 5

were non-motile. The 7 E. coli O157:H7 isolates belonged to 3 phage types: PT14

(3 isolates), PT34 (1 isolate), and PT54 (3 isolates) (Fig. 1). Interestingly, 6 of those 7 E. coli O157:H7 isolates belonged to two of the most common phage types associated with severe human illness in Europe and Canada [START_REF] Mora | Serotypes, virulence genes and intimin types of Shiga toxin (verocytotoxin)-producing Escherichia coli isolates from minced beef in Lugo (Spain) from 1995 through 2003[END_REF]. Six distinct PFGE types (1 to 6) with a high degree of similarity (>86%)

were found among the 7 E. coli O157:H7 isolates recovered from wild boars (Fig. 1). The PT14 and PT34 isolates shared 96% of similarity, with two indistinguishable PFGE types and other two which differed only in ≤2 restriction fragments (Fig. 1). These PFGE types were compared with those found by us in E. coli O157:H7 strains isolated from human patients with diarrhoea living in the same geographic area (Martínez et al., 2009b). It is interesting that the PFGE type of the O157:H7 stx 2 eae-γ1 ehxA isolate belonging to PT54 recovered from the faeces of a hunter-harvested wild boar in November (PFGE type 5) was indistinguishable from that found in an O157:H7 stx 2 eae-γ1 ehxA isolate belonging to the same phage type recovered from a patient in the same area in December (Fig. 1). In the absence of epidemiologic data, these 2 isolates were also tested with multilocus variable-number tandem repeat analysis (MLVA) which fully confirmed the PFGE results (Martínez et al., 2009a).

The common carriage of E. coli O157:H7 and non-O157 STEC indicates that hunted wild boars are a potential source of human infection, since the initial microbiological condition of the carcasses from hunted animals is generally affected by several highly variable factors and so contamination of the meat obtained from them with such pathogens would be frequent. Nevertheless, only

  using the full range of O (O1 to O185) and H (H1 to H56) antisera. All antisera were absorbed with corresponding cross-reacting antigens to remove non-specific agglutinins. The O antisera were produced in the Laboratorio de Referencia de E. coli (Lugo, Spain) and the H antisera were obtained from the Statens Serum Institut (Copenhagen, Denmark).

  of E. coli O157:H7 isolates was performed as described by[START_REF] Khakhria | Extended phage-typing scheme for Escherichia coli O157:H7[END_REF] using phages provided by the National Microbiology Laboratory (Public Health Agency of Canada, Winnipeg, Canada).

  study was supported by grants from the Junta de Extremadura and FEDER (grant 3PR05A009-III Plan Regional de Investigación), from the Xunta de Galicia (grants PGIDIT065TAL26101PR and 07MRU036261PR), from the Ministerio de Educación y Ciencia (AGL-2008-02129), and from the Fondo de Investigación Sanitaria (Instituto de Salud Carlos III, Ministerio de Sanidad y Consumo, Spanish Network for the Research in Infectious Diseases, REIPI, RD06/0008-1018).

  producing Escherichia coli shedding in sheep feces: persistence of specific clones in sheep flocks.Appl. Environ. Microbiol. 75, 1769-1773. Wahlström, H., Tysén, E., Olsson Engvall, E., Brändström, B., Eriksson, E., Mörner, T., Vagsholm, I., 2003. Survey of Campylobacter species, VTEC O157 and Salmonella species in Swedish wildlife.Vet. Rec. 153,[74][75][76][77][78][79][80]

Fig. 1 .

 1 Fig. 1. Dendrogram generated with InfoQuestFP software showing the PFGE-

Acknowledgements

We thank J.M. Benítez, M. Cortés, and W.L. García for their cooperation during the field work. We also thank R. Rubio and A. Aladueña for their skilful technical assistance. S. Sánchez acknowledges the Consejería de Educación y Ciencia de la Junta de Comunidades de Castilla-La Mancha and Fondo Social Europeo for his research fellowship (09/02-C). R. Martínez acknowledges the Junta de Extremadura for his research fellowship (PRE06053). A. Mora acknowledges the Ramón y Cajal programme from the Ministerio de Educación y

A c c e p t e d M a n u s c r i p t 9 few reports have been published on the contamination of pork from wild boar or venison with STEC [START_REF] Piérard | Virulence factors of verocytotoxin-producing Escherichia coli isolated from raw meats[END_REF][START_REF] Miko | Assessment of Shiga toxin-producing Escherichia coli isolates from wildlife meat as potential pathogens for humans[END_REF]. In addition, the finding of indistinguishable PFGE types (and MLVA types) in E. coli O157:H7 isolates recovered from samples from a wild boar and from a human patient in the same area and period suggests that wild boars in this geographic area may play a role in human infections with E. coli O157:H7. However, further studies will be required to further elucidate the degree of zoonotic risk posed. These findings may also have implications in the development of programs for controlling STEC and E. coli O157:H7 at the farm level, since wild boar populations in the studied areas have access to the same pastures as cattle and sheep, and therefore interactions between them will likely lead to interspecies transfer.

Conflict of interest statement

None of the authors of this paper has a financial or personal relationship with other people or organisations that could inappropriately influence or bias the content of the paper.


Volker Kaden
email: volker.kaden@fli.bund.de

Elke Lange

Heike Küster

Thomas Müller

Bodo Lange

An update on safety studies on the attenuated "RIEMSER ® Schweinepestoralvakzine" for vaccination of wild boar against classical swine fever

Keywords: classical swine fever, C-strain oral vaccine, safety, target and non-target species

The RIEMSER ® Schweinepestoralvakzine is an attenuated vaccine for oral vaccination of wild boar against classical swine fever (CSF). The safety of this licensed bait vaccine which is based on the CSF virus (CSFV) strain "C" was investigated in 8 animal species, e.g. weaner pigs (n = 111), wild boar (n = 11), ruminants (cattle, goats and sheep, n = 11), foxes (n = 5), rabbits (n = 12), and mice (n = 10). Animals were vaccinated either with a single vaccine dose containing at least 10 4.5 TCID 50 , or with overdoses, i.e. the tenfold dose, or they were subjected to repeated application schemes. During the entire observation period none of the animals which were given the vaccine virus showed clinical signs, with the exception of rabbits. These reacted to the vaccination with fever. Orally vaccinated pigs did not transmit vaccine virus to susceptible contact animals (sentinels).

In none of the species examined neither vaccine virus nor viral RNA could be detected in blood after vaccination. In one wild boar viral RNA could be established in the tonsil 21 days post-vaccination (dpv); all other organ samples tested virologically negative. Up to 77.5% of the pigs and wild boar developed virus neutralising antibodies (VNA) already 14 dpv. The mean VNA titres observed in the vaccination groups seemed to depend rather on individual factors than on the administered virus dose (virus titre per dose) or the vaccination scheme. These results are comparable with findings obtained during oral vaccination campaigns in wild boar and after parenteral vaccination with this C-strain virus. From the results presented here it can be concluded that RIEMSER ® Schweinepestoralvakzine is safe for target and non-target species.

A c c e p t e d M a n u s c r i p t

Introduction

Classical swine fever (CSF) is a highly contagious viral disease of domestic pigs and wild boar which occurs especially in areas with a high population density. Independently of the currently auspicious epidemiological CSF situation in Central and Western Europe, the disease occurs worldwide. In the 1970s and 1980s, prophylactic and emergency vaccinations with safe and effective live vaccines played an essential role in the eradication of CSF in many parts of the world, including Europe. Since 1990, control and eradication of CSF in the European Union (EU) have been based on a non-vaccination and stamping-out strategy [START_REF] Laddomada | Incidence and control of CSF in Europe[END_REF][START_REF] Moennig | Introduction to classical swine fever virus, disease and control policy[END_REF]. In compliance with Council Directive 2001/89/EC [START_REF] Anonymous | Council Directive 2001/89/EC on Community measures for control of classical swine fever, 23 October[END_REF] routine vaccinations of domestic pigs against CSF are prohibited in the EU, however, emergency vaccination can be permitted if an extensive spread of CSF virus (CSFV) with subsequent high economic losses is to be expected. In contrast, vaccines against CSF are still widely used in domestic pigs in Asia and South America.

The control of CSF in wild boar populations is much more complicated than in domestic pigs, especially in regions with a high population density of wild boar. In such regions, the disease can persist over a relatively long period of time, as observed in Germany in the 1990s. Currently, several strategies for the control of CSF in wild boar are used. One of them includes the oral vaccination of wild boar in the frame of emergency vaccination combined with a reduction of the population density. This strategy was used in Germany at first [START_REF] Kaden | Oral immunisation of wild boar against classical swine ferver: evaluation of the first field study in Germany[END_REF]. According to Council Directive 2001/89/EC [START_REF] Anonymous | Council Directive 2001/89/EC on Community measures for control of classical swine fever, 23 October[END_REF] oral emergency vaccination of wild boar is permitted if the above-mentioned conditions are fulfilled and the vaccination plan has been approved by the European Commission. Disease control via oral vaccination, however, is labourintensive and requires safe and effective live vaccines (Chenut et al., 1999;[START_REF] Kaden | Oral immunisation of wild boar against classical swine ferver: evaluation of the first field study in Germany[END_REF][START_REF] Kaden | Oral immunisation of wild boar against classical swine fever: concluding analysis of the recent field trials in Germany[END_REF] in a formulation suitable for wild boar of all A c c e p t e d M a n u s c r i p t age classes [START_REF] Kaden | Oral immunisation of wild boar against classical swine fever: concluding analysis of the recent field trials in Germany[END_REF]Brauer et al., 2006). A better alternative to the currently existing modified live virus vaccines would be a safe and effective DIVA vaccine which permits to differentiate vaccinated from infected animals. Therefore, research on the development of live DIVA vaccines has been intensified in the past few years and several vaccine candidates for oral vaccination have been investigated (Koenig et al., 2007b;[START_REF] Wehrle | Chimeric pestiviruses: candidates for live-attenuated classical swine fever marker vaccines[END_REF][START_REF] Kaden | Oral vaccination against classical swine fever with a chimeric Pestivirus: comparative investigations of liquid and lyophilised virus[END_REF][START_REF] Leifer | Modified live marker vaccine candidate CP7_E2alf provides early onset of protection against lethal challenge infection with classical swine fever virus after intramuscular and oral immunisation[END_REF]. However, licensed CSF marker vaccines suitable for oral application in wildlife are not available yet.

The efficacy of the RIEMSER ® Schweinepestoralvakzine, a conventional CSF live vaccine based on the "C" strain was demonstrated in various studies [START_REF] Kaden | Oral immunisation of wild boar against classical swine ferver: evaluation of the first field study in Germany[END_REF][START_REF] Kaden | Oral immunisation of wild boar against classical swine fever: concluding analysis of the recent field trials in Germany[END_REF][START_REF] Kaden | Evaluation of the oral immunisation of wild boar against classical swine fever in Baden-Württemberg[END_REF][START_REF] Kern | Oral Immunisierung gegen klassische Schweinepest (KSP) beim Schwarzwild in Brandenburg 1995 bis 1997[END_REF][START_REF] Von Rüden | Retrospective analysis of the oral immunisation of wild boar populations against classical swine fever virus (CSFV) in region Eifel of Rhineland-Palatinate[END_REF] and resulted in the licensing of this bait vaccine in Germany in 2005. So far, there are no reports on experimental safety studies with this vaccine. Therefore, this paper intends to provide information on safety studies of the German CSF oral vaccine (RIEMSER ® Schweinepestoralvakzine) including virological and serological investigations in line with selected safety experiments carried out in past years. As there are no guidelines for the licensing of CSF oral vaccines in the European Union, safety studies were carried out according to the European Pharmacopoeia 5.0 "Swine-fever vaccine (live), classical, freeze-dried" [START_REF] Anonymous | Klassische-Schweinepest-Lebend-Impfstoff (gefriergetrocknet), Vaccinum pestis classicae suillae vivum cryodesticcatum[END_REF], which was in force during the study period, and the national guideline for licensing and testing of batches of CSF live vaccines (edited by the former Federal Research Centre for Virus Diseases of Animals, Tübingen, 1985), both destined for parenteral administration. Furthermore, the specific conditions of oral vaccination in the field were taken into account.

A c c e p t e d M a n u s c r i p t

Materials and methods

Vaccine

The CSF oral vaccine used (RIEMSER ® Schweinepestoralvakzine, RIEMSER Arzneimittel AG, Greifswald-Insel Riems, Germany) is based on the lapinised and attenuated C (Chinese) strain and was provided by the All-Russian State Centre for Quality and Standardisation of Veterinary Drugs and Food (Moscow, Russia) in 1977. After several hundred serial passages in rabbits, the vaccine strain was adapted to primary porcine foetal kidney cells first and subsequently to permanent porcine kidney cells, which later on were also used for propagation of the commercial oral vaccine virus. This vaccine is filled into blisters (about 1.6 ml vaccine per blister), which are covered with a cereal-based bait matrix (size of the bait: 4 x 4 x 1.6 cm). A total of 12 different vaccine batches were used for the individual experiments. The vaccine dose contained at least 10 4.5 tissue culture infection doses 50 (TCID 50 ).

Animals

For the safety studies 111 weaner pigs (87 vaccinated and 24 sentinel animals) aged 6-7 weeks, 11 wild boars aged 3.5-11 months, three bovines aged 1-2 years (breed German Simmental, Holstein-Friesian), three goats of mixed sex aged 6-30 months (German Improved White breed), 5 sixmonth-old sheep of mixed sex (German Improved Land breed), 12 rabbits (breed: Russians, mixed sex, 6 months old), 10 white mice (3 months old), and 5 young red foxes (Lupus lupus) at the age of 8 months were used. Whereas wild boar, goats, rabbits and mice were derived from our own breeding unit, domestic pigs, cattle, sheep and foxes were purchased from commercial farms in the federal states of Mecklenburg-Western A c c e p t e d M a n u s c r i p t Pomerania and Saxony. Prior to the experiments the animals were tested negative for antibodies to pestiviruses using virus neutralisation test (VNT). All animals were monitored daily for clinical signs. Rectal temperature was also taken daily in all animals except for wild boar, foxes and mice. Body weight was partially monitored (see Table 1). At the end of the experiments the animals were either euthanised for necropsy or re-used for other studies, e.g. for efficacy testing of vaccine batches. Generally, animals were randomized into the individual groups. All handling and invasive procedures were conducted in compliance with the German Animal Welfare Act.

Experimental design 2.3.1. Safety studies in domestic pigs and wild boar 2.3.1.1 Safety of one vaccine dose

Eight wild boars and 3 groups of 5 weaner pigs each were held in separate pens and vaccinated orally with one vaccine dose (equivalent to 1 vaccine bait) using three different batches (nos. 220600, 230600 and 240600). One day post-vaccination (dpv), 5 unvaccinated control animals were brought into contact with domestic pigs of each vaccination group to investigate the shedding of vaccine virus by vaccinated animals.

Seroconversion after vaccination was examined 14 (pigs, wild boar) and 28 dpv (wild boar and contact controls) by VNT.

Safety of one overdose of the vaccine

A c c e p t e d M a n u s c r i p t

Forty-two weaner pigs and 3 wild boars were vaccinated orally with one overdose, i.e. 10 vaccine doses. Three groups of 4 pigs each were vaccinated with the three batches mentioned above (2.3.1.1) and brought into contact with two unvaccinated animals on day 2 after vaccination.

Additionally, groups of 3 pigs each were vaccinated with 8 different batches (370203, 380203, 390303, 0560105, 0570105, 731206, 741206 and 751206), whereas three wild boars were immunised with one overdose of another batch (640206). Virus neutralising antibody titres were determined on the day of vaccination, 14 and/or 21 dpv as well as 28 dpv (only contact controls). At necropsy, EDTA blood and organs (tonsil, spleen, kidney, mandibular and mesenteric lymph nodes, lung, bone marrow) were collected from all wild boar and selected domestic pigs for detection of CSFV or viral RNA.

Safety after repeated vaccination

In one experiment 5 weaner pigs were vaccinated twice with one oral vaccine dose at an interval of 14 or 28 days using three different batches (220600, 230600 and 240600). Blood samples were taken on days 0, 14, 28, 42, 56, 84 and 112 days after the first vaccination (dpv 1 ) for detection of antibodies.

In another experiment, six weaner pigs each received one overdose of vaccine batch no. 741206 at an interval of four days. The vaccinated animals were kept together with three sentinels beginning one day after the second vaccination. Blood samples were taken 21 dpv 1 .

Safety studies in cattle, goats, sheep, rabbits, foxes and mice

A c c e p t e d M a n u s c r i p t Cattle, goats and sheep were vaccinated orally with the 2.5-fold vaccine dose. Furthermore, one bait was offered in a feeding trough for free uptake.

Blood was collected 0, 26 and 40 dpv for determination of VNA titres.

The rabbits (n = 8) were inoculated orally with 1.0 ml RIEMSER ® Schweinepestoralvakzine by direct administration into the mouth cavity using a syringe. On day 1 after oral vaccination, animals were brought into contact with 4 unvaccinated conspecifics (sentinels). Blood samples were collected 0, 14, 20 and 35 dpv.

For vaccination of mice, animals were kept in separate cages and offered ad libitum 1 vaccine dose (i.e. 1.6 ml) diluted in 10 ml drinking water. The animals were bled for detection of VNA at necropsy, 21 dpv. Foxes, kept individually in catches, were offered one vaccine bait and successful bait uptake was recorded. Blood samples were collected 21 dpv for serological investigations.

Serological and virological investigation of samples

Antibody detection

Antibodies were detected by means of VNT as described by [START_REF] Kaden | Oral immunization of pigs against classical swine fever. Course of the disease and virus transmission after simultaneous vaccination and infection[END_REF]. In order to detect homologous VNA titres the C-strain vaccine virus was used instead of the CSFV strain Alfort 187.

Detection of vaccine virus or viral RNA

A c c e p t e d M a n u s c r i p t

Re-isolation of the vaccine virus from blood and organ tissues was carried out on confluent permanent EFN-R cells (CCLV, RIE 86) (Kaden et al., 2004b), whereas for detection of viral RNA a real-time RT-PCR (rtRT-PCR) protocol established for routine diagnosis and validated by the National Reference Laboratory for CSF was used (Hoffmann et al., 2005). The presence of antigen of the vaccine virus in bone marrow smears was detected by an indirect immunofluorescence test [START_REF] Ahrens | Efficacy of the classical swine fever (CSF) marker vaccine Porcilis ® Pesti in pregnant sows[END_REF] using a mouse-anti-CSFV-E2 monoclonal antibody and a polyclonal FITClabelled goat anti-mouse antibody (DAKO Cytomation, Gilestrup, Denmark) as conjugate.

Statistical analysis

The statistical analysis was carried out with the statistics program SigmaStat 3.0 (SPSS Science Software gmb, Erkrath, Germany). The results were considered statistically significant when p <0.05.

Results

Safety in domestic pigs and wild boar

Domestic pigs and wild boar inoculated with one vaccine dose, one overdose (10-fold vaccine dose) or/and repeated vaccination showed no clinical signs during the entire observation period. All animals showed an increase in body weight as recorded in Table 1. The increase of the mean body weight of pigs vaccinated with 10 doses (one overdose) was slightly lower than in the control group on day 28 post-vaccination, however, A c c e p t e d M a n u s c r i p t these differences were not significant. In contrast, the animals vaccinated with one dose showed a significant higher increase of the mean body weight 28 dpv.

In general, the rectal temperatures of pigs vaccinated with a single dose or one overdose remained within the normal range after vaccination as shown in Fig. 1 for one overdose (three batches). A small number of piglets reacted with a slight and temporary increase in body temperature independently of the time of vaccination, but did not develop fever. No gross lesions as a result of the vaccine application were found at necropsy, neither in domestic pigs nor in wild boar. However, catarrhal pneumonia in apical lobes was detected in individual vaccinated and control piglets.

Virus isolation or detection of viral RNA in EDTA blood of vaccinated pigs showed a negative result. Only the tonsil of one wild boar turned out to be positive in rtRT-PCR 21 dpv with a Ct value of 38.4, whereas all other organ and blood samples of vaccinated pigs and wild boars scored virologically negative.

Most of the domestic pigs and wild boars showed moderate development of VNA 14 days after administration of one vaccine dose with mean VNA titres ranging between 1:24 and 1:55. In the wild boar group, VNA titres drastically increased 14 days later. Repeated vaccination at intervals of 14 and 28 days resulted in high mean VNA titres 28 dpv but there were no significant differences between both groups (Table 2). After vaccination with one overdose relatively low mean VNA titres in wild boars and in three groups of weaner pigs were detected 21 dpv, however, no correlation was observed between the virus titre of the individual vaccine batches and the induced mean antibody titres (Table 3).

All sentinels kept in contact with pigs vaccinated orally with C-strain vaccine remained healthy and did not develop antibodies against the vaccine virus.

A c c e p t e d M a n u s c r i p t

Safety in other species

Whereas cattle accepted the vaccine baits very well, goats and sheep showed a delayed bait uptake. The bait vaccine neither induced clinical signs nor an increase in body temperature in these species (data not shown). Whereas goats and sheep did not develop antibodies against the vaccine virus, two of three bovines developed an immune response resulting in low VNA titres of 1:8 and 1:11 at 26 dpv and 1:32 and 1:181 at 40 dpv, respectively.

Vaccinated rabbits reacted with moderate fever (40.20.32°C) and slight apathy as well as short anorexia during the febrile state. In contrast, sentinel rabbits neither showed clinical symptoms and fever (mean rectal temperature: 38.50.28°C) nor seroconversion (data not shown). Table 4 shows the seroconversion of vaccinated rabbits.

Foxes and mice remained healthy after oral administration of C-strain vaccine and did not develop neutralising antibodies (data not shown).

Discussion

The high safety of live-attenuated C-strain vaccines for domestic pigs has been demonstrated worldwide in many cases [START_REF] Bognár | Experiences with a "Chinese" strain of lapinized swine fever virus[END_REF][START_REF] Bran | Sur la stabilité de quelques caractères biologiques de la souche C de virus lapinisé de la peste porcine[END_REF][START_REF] Tielen | Een onderzoek naar eventuele schadelijke neveneffecten van de enting van varkens met een levend vaccin (C-stam) tegen varkenspest[END_REF][START_REF] Précausta | Pest porcine classique: Quelques notions complementaires sur l'innocuite de la souche chinoise CL[END_REF][START_REF] Beer | Die Immunprophylaxe und -metaphylaxe gegen Schweinepest in der Deutschen Demokratischen Republik mit Schweinepest-Lebendvirusvakzine "Riems[END_REF][START_REF] Lin | An overall report on the development of a highly safe and potent lapinized hog cholera virus strain for hog cholera control in Taiwan[END_REF]Glaner et al., 1984;[START_REF] Terpstra | Development and properties of a cell culture produced vaccine for hog cholera based on the Chinese strain[END_REF]Dahle and Liess, 1995 and others). These vaccines are also known to have a high efficacy in CSF control in domestic pig populations (summarised by [START_REF] Aynaud | Principles of vaccination[END_REF][START_REF] Van Oirschot | Vaccinology of classical swine fever: from lab to field[END_REF]. Although oral vaccination of wild boar with the C-strain vaccine (RIEMSER ® Schweinepestoralvakzine)

A c c e p t e d M a n u s c r i p t has been carried out for almost 15 years without any problems in Germany [START_REF] Kaden | Oral immunisation of wild boar against classical swine ferver: evaluation of the first field study in Germany[END_REF][START_REF] Kaden | Oral immunisation of wild boar against classical swine fever: concluding analysis of the recent field trials in Germany[END_REF][START_REF] Kaden | Diagnostic procedures after completion of oral vaccination against classical swine fever in wild boar[END_REF] and other European countries there were concerns with regard to the safety of this vaccine for wild boar and other wildlife species.

Safety studies described here clearly demonstrate that this vaccine is safe for domestic pigs and wild boar as no effect on the general health status or the growth of vaccinated animals was seen. However, as expected pigs with a higher initial body weight showed a more considerable weight gain 28 dpv than animals with a lower initial body weight. Also, no batch-related influence on the development of the body weight was observed. The absence of virus shedding after parenteral vaccination of the C-strain vaccine had already been proven (Glaner et al., 1984;Dahle and Liess, 1995;Koenig et al., 2007). Our study provides further evidence that the vaccine virus is not shed in secretions and excretions of vaccinated animals since none of the sentinel pigs kept in contact with vaccinated animals developed antibodies in any of the experiments conducted. These results confirm findings by Chenut et al. (1999) and previous own experiences (Kaden et al., 2004b), according to which neither virus nor viral RNA was detected in faeces and nasal swabs after oral application. Interestingly, in our study vaccine virus was only found 21 dpv by means of rtRT-PCR in the tonsil of one orally vaccinated animal but not in blood. This may indicate that the C-strain virus only replicates at a low level after oral vaccination.

However, in previous studies vaccine virus could be detected in different organs, mainly in tonsils, spleen and Ln. mandibularis (Kaden et al., 2004b). A recent parenteral vaccination study suggests that the C-strain virus may persist for relatively long periods in individual domestic pigs, as proven by the detection of viral RNA in blood and tonsils up to 14 dpv and 42 dpv, respectively, whereas virus isolation succeeded only up to 6 dpv (Koenig et al., 2007a). In contrast, C-strain virus and viral RNA were only detectable for 8 or 9 days after oral vaccine intake (Kaden et al., 2004b).

However, viral RNA can also be detected for a relatively long time in individual orally vaccinated pigs, in experimentally vaccinated animals up to A c c e p t e d M a n u s c r i p t 35 dpv and in field samples derived from wild boar for up to 32 days after distribution of vaccine baits (Kaden et al., unpublished). However, the virus strain does not replicate in bone marrow as the recent study and previous investigations (Fischer et al., 1991) demonstrate. These findings indicate that attenuated C-strain virus may take a different pathway than virulent CSFV.

The seroconversion of animals vaccinated orally with one dose shows a similar course as after parenteral vaccination (Dahle and Liess, 1995), however, only 77.5% of pigs and wild boar developed antibodies 14 dpv. About 87% (34 out of 38) of the vaccinated animals turned seropositive on day 28 pv. The kinetics of VNA provides evidence that the onset of the immune response after oral vaccination of pigs with one vaccine dose is delayed compared to parenteral vaccination. The differences in the mean VNA titres observed in individual groups of pigs after oral administration of overdoses cannot be explained yet. We suppose that these differences in VNA titres are based on the individual immunological reactivity of the animals and/or incomplete vaccine uptake. The large standard deviations of VNA titres obtained in individual groups may underline this presumption. Oral vaccination of pigs at intervals of 14 or 28 days did not lead to significant differences in VNA titres. These findings support previous investigations obtained with a small wild boar group (Kaden et al., 2004a). Cattle, sheep, goats, as well as foxes and mice were used as model species for wildlife species which under field conditions might be bait competitors. None of these animals developed clinical signs and fever (rectal temperature only checked in ruminants) as a result of vaccination and bait uptake. Therefore, C-strain live vaccine also seems to be safe for these non-target species, albeit this assessment is only based on a limited number of investigated animals. As expected, orally vaccinated rabbits developed a significant increase in rectal body temperature on days 3 and/or 4 and a reduced food intake after administration of lapinised C-strain A c c e p t e d M a n u s c r i p t virus; slightly later than after intravenous inoculation (Lange, unpublished). Chenut et al. (1999) also observed fever in rabbits after oral administration of C-strain virus, occurring slightly later than in our study. Most likely, the lower antigen content (10 3 pig PD 50 ) of the vaccine virus used by Chenut et al. (1999) is the reason for the delayed increase in rectal body temperature. Regarding seroconversion in non-target species, only cattle and rabbits developed neutralising antibodies after oral intake of C-strain vaccine. Foxes remained seronegative after intake of vaccine baits. This result was expected and agrees with findings of Dewulf et al. (2001) after infection of dogs, cats and rats with CSFV as these species as well as foxes are not the natural host for CSFV.

In conclusion, results presented here and experiences during oral vaccination of wild boar against CSF in the field suggest that the CSF oral vaccine (RIEMSER ® Schweinepestoralvakzine) based on the CSFV strain "C" is safe for the target species, i.e. wild boar and domestic pigs, as well as for relevant non-target wildlife. As the vaccine virus is genetically very stable, there is no risk of reversion to virulence [START_REF] Aynaud | Principles of vaccination[END_REF] and development of new virus types caused by recombination of vaccine and field virus is considered very low.

A c c e p t e d M a n u s c r i p t Brauer, A., Lange, E., [START_REF] Kaden | Diagnostic procedures after completion of oral vaccination against classical swine fever in wild boar[END_REF]. Oral immunisation of wild boar against classical swine fever: uptake studies of new baits and investigations on the stability of lyophilised C-strain vaccine. Eur. J. Wildl. Res. 52, 271-276. Chenut, G., Saintilan, A.-F., Burger, C., Rosenthal, F., Cruciére, C., Picard, M., Bruyére, V., Albina, E., 1999. Oral vaccination of swine with a classical swine fever vaccine (Chinese strain) and transmission studies in rabbits and sheep. Vet. Microbiol., 64, 265-276. Dahle, J., Liess, B., 1995. Assessment of safety and protective value of a cell culture modified strain "C" vaccine of hog cholera/classical swine fever virus. Berl. Münch. Tierärztl. Wschr. 108, 20-25. Dewulf, J., Laevens, H., Koenen, F., Mintiens, K., de Kruif, A., 2001. Evaluation of the potential of dogs, cats and rats to spread classical swine fever virus. Vet. Rec. 149, 212-213. Glaner, M., Kaden V., Tesmer, S., Hahnefeld, H., 1984. The vaccine against porcine cholera ("Riemser Schweinepest-Vakzine") -a cell culture vaccine of a high immunobiological valency. Medicamentum, special issues for veterinary science, 21-25. Hoffmann, B., Beer, M., Schelp, C., Schirrmeier, H., Depner, K., 2005

Fischer

  , U.,Kaden V., Beyer, J., 1991. Zur Nachweissicherheit von Schweinepestantigen und zur Differenzierung der Feld-und Vakzinevirusinfektion mit dem direkten Immunofluoreszenztest an Organmaterial.[133][134][135][136]

  . Validation of a real-time RT-PCR assay for sensitive and specific detection of classical swine fever. J. Virol.Methods 130,[36][37][38][39][40][41][42][43][44]

  Fig. 1 Mean rectal temperatures of pigs vaccinated with one overdose

Table 3 .

 3 Seroconversion after application of the tenfold dose (one overdose)

	Application scheme	Species	Batch no.	Virus content per		Mean VNA titres (ND 50 )
				dose (bait)	0 dpv	14 dpv	21 dpv
				(log 10 TCID 50 )
	Once	Pigs	370203	5.25	neg	nt	286+212.6
		Pigs	380203	5.5	neg	nt	298.7+125.5
		Pigs	390203	5.5	neg	nt	188.3+64.3
		Pigs	560105	6.0	neg	nt	178.3+164.4
		Pigs	570105	6.3	neg	nt	100.3+47.9
		Pigs	220600	4.5	neg	111.4+132.1	nt
		Pigs	230600	4.8	neg	116.0+128.3	nt
		Pigs	240600	4.8	neg	112.4+131.2	nt
		Pigs	731206	6.7	neg	nt	44.3+20.5
		Pigs	741206	6.5	neg	nt	35.2+28.0
		Pigs	751206	6.3	neg	nt	40.3+43.7
		Wild boar	640206	6.3	neg	33.0+17.9	66.0+35.3
	Twice (interval of 4 days)	Pigs	741206	6.5	neg	nt	33.3+11.1
	nt = not tested

Table 4 .

 4 Seroconversion in rabbits after application of CSF oral vaccine

	2
	3
		dpv	Number of	Mean VNA titres (ND 50 ) per vaccination
			seropositive animals	group 2
			per group
		0	0/8	negative
		14	4/6 1	30.5+16.7
		20	5/8	256.0+0
		35	5/8	256,0+0
	4
	5	1 no serum from two animals
	6	2 seropositive animals
	7

Acknowledgements

The authors thank Sybilla Welsch and Brigitte Dannenfeld for excellent technical assistance. We gratefully acknowledge Anette Beidler and Wolfgang Boehle for critical review of the manuscript.