Related papers: On non-holonomic systems and variational principle…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
This paper studies nonsmooth variational problems on principal bundles for nonholonomic systems with collisions taking place in the boundary of the manifold configuration space of the nonholonopmic system. In particular, we first extended…
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus…
We establish the procedure to derive from an action-based variational principle the classical equations of motion in Hamiltonian phase space of a particle subject to general position and velocity dependent non-holonomic equality…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
Formulating the equations of motion for cosmological bodies (such as galaxies) in an integral, rather than differential, form has several advantages. Using an integral the mathematical instability at early times is avoided and the boundary…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
We consider the dynamics of systems of self propelling particles with nonholonomic constraints. A continuum model for a discrete algorithm used in works by T. Vicsek et al. is proposed. For a case of planar geometry the finite flocking…
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
For the first time, both non-holonomic and quasi-integrable deformations are obtained for the AB system of coupled equations. The AB system models geophysical and atmospheric fluid motion along with ultra-short pulse propagation in…
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…
When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the…
We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle…
We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. In the light of this concept we describe dynamics of the collisions. Several applications have been investigated.…