Multistability, scattering and selection of equilibria in the mechanical system with constraint

Abstract

Nonlinear phenomena caused by a one-parameter family of steady-states are under investigation. We consider a mechanical system with constraint defined by a surface (like a Mexican hat) in the three–dimensional space. The corresponding system of the ordinary differential equations has an ellipse of stable equilibria and demonstrates strong multistability. We study the realization of equilibria under linear damping through numerical simulation. Our results indicate the complicated behaviour of trajectories when initial energy is high, and/or damping is low. In this case, the realization of equilibria strongly depends on the initial state of the system and demonstrates chaotic scattering. We explain these phenomena as a memory effect about conservative chaos at zero friction.