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

• Published in: Communications in nonlinear science & numerical simulation Vol. 95; p. 105602
• Main Authors: Govorukhin, V.N., Tsybulin, V.G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2021; Elsevier Science Ltd
• Subjects: Chaos; Chaos theory; Cosymmetry; Damping; Differential equations; Energy; Family of equilibra; Friction; Linear damping; Mechanical properties; Mechanical systems; Memory effects; Multistability; Nonlinear equations; Nonlinear phenomena; Scattering; Simulation; Chaos; Multistability; Family of equilibra; Memory effects; Cosymmetry; Scattering
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105602

•A mechanical system with constraint defined by a surface in the space is studied analytically and numerically.•This system demonstrates strong multistability due to a one-parameter family of stable steady states.•The realization of equilibria under linear damping strongly depends on the initial state with chaotic scattering.•We explain these phenomena as a memory effect about conservative chaos at zero friction. 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.