多体系统动力学约束Hamilton方程多步块方法  

Multistep block method for constrained Hamilton’s equations of multibody system dynamics

作　　者：杜文静 丁洁玉 Du Wenjing;Ding Jieyu(School of Mathematics and Statistics,Qingdao University,266071,Qingdao,China;Center for Computational Mechanics and Engineering Simulation,Qingdao University,266071,Qingdao,China)

机构地区：[1]青岛大学数学与统计学院,青岛266071 [2]青岛大学计算力学与工程仿真研究中心,青岛266071

出　　处：《应用力学学报》2021年第3期1016-1021,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11772166,11472143)。

摘　　要：针对多体系统动力学Hamilton体系正则微分-代数方程,基于等距节点、Chebyshev节点、Legendre节点等非等距节点,在时间区间上建立r-级多步块求解格式,得到单步区间各节点的非线性代数方程,求解过程利用Newton迭代。以双连杆机械臂系统为例,使用r-级多步块格式进行数值仿真,通过改变步长、仿真时间以及节点数分别对指标-1、-2、-3的Hamilton系统正则微分-代数方程进行数值验证。数值结果表明,本文方法稳定性好、精度高、计算效率高,能很好保持Hamilton能量误差以及各级约束误差,特别是对于长时间仿真,Hamilton能量误差不会产生漂移,适合长时间多体系统动力学仿真。Based on the equidistant nodes and non-equidistant nodes such as Chebyshev nodes and Legendre nodes,an r-stage multi-step block method is established in time interval for the regular differential-algebraic equation of the Hamiltonian system in multibody system dynamics.The nonlinear algebraic equation of each node in a single step interval is obtained.Newton’s iteration is used in the solution process.The method is L-stable.Taking the two-link manipulator system as an example,the numerical simulation is carried out by using the r-stage multi-step block scheme.By changing the step size,simulation time and the number of nodes,regular differential-algebraic equations of the index-1,-2,-3,respectively,are verified.The numerical results show that this method has good stability,high precision and high efficiency,and can keep the Hamilton energy error and constraint error.Especially for long-time simulation,Hamiltonian energy error will not drift,so it is suitable for long-time multibody system dynamics simulation.

关 键 词：多体系统动力学 HAMILTON系统 微分-代数方程 多步块方法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O175.1[自动化与计算机技术—计算机科学与技术]