Related papers: Stochastic Chaplygin systems
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint…
A nonholonomic system consists of a configuration space Q, a Lagrangian L, and an nonintegrable constraint distribution H, with dynamics governed by Lagrange-d'Alembert's principle. We present two studies both using adapted moving frames.…
We consider nonholonomic Chaplygin systems and associate to them a $(1,2)$ tensor field on the shape space, that we term the gyroscopic tensor, and that measures the interplay between the non-integrability of the constraint distribution and…
We show that the Suslov nonholonomic rigid body problem can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a…
We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved…
We propose a simple construction of the non-Hamiltonian dynamical systems possessing an invariant measure. These non-Hamiltonian systems are deformations of the Hamiltonian systems associated with trivial deformations of the canonical…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
Via compression ([11, 7]) we write the $n$-dimensional Chaplygin sphere system as an almost Hamiltonian system on $T^*SO(n)$ with internal symmetry group $SO(n-1)$. We show how this symmetry group can be factored out, and pass to the fully…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…
We consider some issues of the representation in the Hamiltonian form of two problems of nonholonomic mechanics, namely, the Chaplygin's ball problem and the Veselova problem. We show that these systems can be written as generalized…
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…
In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system,…
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…
This paper is the third part of our study started with Cattiaux, Le\'{o}n and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained…
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical…
We introduce and study the Chaplygin systems with gyroscopic forces. This natural class of nonholonomic systems has not been treated before. We put a special emphasis on the important subclass of such systems with magnetic forces. The…
A generalisation of Chaplygin's Reducing Multiplier Theorem is given by providing sufficient conditions for the Hamiltonisation of Chaplygin nonholonomic systems with an arbitrary number $r$ of degrees of freedom via Chaplygin's multiplier…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…