非完整约束Hamilton动力系统保结构算法

Abstract

Based on the concept of variational integrator and the Lagrange-d’Alembert principle with dual variables, a high-order structure-preserving algorithm for Hamiltonian systems with nonholonomic constraints was proposed. Based on the variational integrator, a discretization form of the Lagrange-d’Alembert principle with dual variables was obtained by means of appropriate polynomials and quadrature rules. On the basis of this discretization form, a numerical integration method was given with displacements at both ends of the integral interval as independent variables. Meanwhile, the nonholonomic constraints were strictly met at the endpoints of the integral interval and the control points within the interval. The symmetric property of the proposed algorithm was proved. Numerical examples show that, the proposed algorithm has a high convergence order, strictly meets the nonholonomic constraints and has good long-time behaviors.