Preservation of adiabatic invariants and geometric numerical algorithm for disturbed nonholonomic systems

Abstract

Perturbations to Mei symmetry and the numerical algorithm of disturbed nonholonomic systems are studied under total variational discretization. The discrete equations on regular lattices of nonholonomic systems in the undisturbed and the disturbed cases are presented. The determining equations of Mei symmetry are established for undisturbed and disturbed systems. The exact invariants of Noether type led by Mei symmetry for undisturbed nonholonomic systems are given under infinitesimal transformations of Lie groups. For discrete disturbed nonholonomic systems, the condition of existence of adiabatic invariants led by perturbation to Mei symmetry and their forms are presented. The numerical simulations demonstrate that the geometric numerical algorithm has a higher precision and longer time stability than the standard numerical method.