Related papers: The Bouncing Penny and Nonholonomic Impacts

The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…

Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of…

In an ordinary billiard system trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is…

In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…

We have developed a method to study the effects of a perturbation to the motion of a test point--like object in a Schwarzschild spacetime. Such a method is the extension of the Lagrangian planetary equations of classical celestial mechanics…

Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…

In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…

We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…

This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle's Invariance Principle for these systems and state asymptotic stability criteria. We also present some related…

A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…

This work presents the variational principles and the intrinsic versions of several equations in field theories, in particular, for the Classical Euler-Lagrange field equations, the implicit Euler-Lagrange field equations and the…

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…

We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick under certain fixed…

The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and…

We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…