Related papers: On Collisions in Nonholonomic systems

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…

In this paper we study the existence of solutions to an isotropic differential inclusion.

In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…

We note that the non-orthogonality of states and their coincidence at the degeneracy point are both admitted by nonlinear Hermitian systems and linear non-Hermitian systems. These striking characteristics motivate us to re-investigate the…

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison…

The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control parameters. The model considers the dynamics of a bouncing…

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the…

We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their…

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite…

We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…

This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…

In this paper we consider applications of methods from wavelet analysis to nonlinear dynamical problems related to accelerator physics. In our approach we take into account underlying algebraical, geometrical and topological structures of…

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

Progress in the study of collisions of multiply charged ions with surfaces is reviewed with the help of a few recent examples. They range from fundamental quasi-one electron processes to highly complex ablation and material modification…

For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions…

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…

Molecular dynamics calculations of inelastic collisions of atomic oxygen with molecular nitrogen are known to show orders of magnitude discrepancies with experimental results in the range from room temperature to many thousands of degrees…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

We study non-topological solitons, so called Q-balls, which carry a non-vanishing Noether charge and arise as lump solutions of self-interacting complex scalar field models. Explicit examples of new axially symmetric non-spinning Q-ball…