非完整约束Hamilton动力系统保结构算法  

A Structure⁃Preserving Algorithm for Hamiltonian Systems With Nonholonomic Constraints

作　　者：满淑敏 高强[1] 钟万勰[1] MAN Shumin;GAO Qiang;ZHONG Wanxie(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian,Liaoning 116023,P.R.China)

机构地区：[1]大连理工大学工程力学系,工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《应用数学和力学》2020年第6期581-590,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11972107,91748203);中央高校基本科研业务费(DUT2019TD37)。

摘　　要：基于变分积分的思想和对偶变量表示的Lagrange-d’Alembert原理,构造了一类求解非完整约束Hamilton动力系统的高阶保结构算法.基于变分积分法,选取适当的多项式及数值积分方法,将对偶变量形式的Lagrange-d’Alembert原理进行离散.在此离散原理的基础上,以积分区间两端位移为独立变量,同时要求在区间端点处及区间内部的控制点处严格满足非完整约束,从而得到数值积分方法.给出了算法的对称性证明.数值算例表明算法具有高阶收敛性,严格满足非完整约束,且在长时间仿真后,依然能保持良好的数值性质.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 appro⁃priate polynomials and quadrature rules.On the basis of this discretization form,a numerical in⁃tegration method was given with displacements at both ends of the integral interval as independ⁃ent 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.

关 键 词：非完整约束 变分积分 保结构算法 对偶变量 

分 类 号：O241[理学—计算数学]