High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints

Abstract

Based on the Lagrange–d’Alembert principle and a modified Lagrange–d’Alembert principle, two kinds of symmetric algorithms with arbitrary high order are proposed for non-holonomic systems. The modified Lagrange–d’Alembert principle is constructed by adding an augment term to the Lagrange–d’Alembert principle, so that the non-holonomic constraints can be directly derived from variation. The high order algorithms are constructed by: (1) choosing control points to approximate generalized coordinates and Lagrange multipliers; (2) performing quadrature rules to approximate integrals; (3) choosing constraint points to satisfy non-holonomic constraints. The order of the presented algorithms is investigated numerically. The main factors to affect the accuracy of proposed algorithm were analyzed. Furthermore, the numerical algorithms are proven to be symmetric and can satisfy non-holonomic constraints with high precision.