非完整系统动力学仿真θ_1方法研究  

RESEARCH ON θ_1 METHOD FOR DYNAMICS SIMULATION OF NON-HOLONOMIC SYSTEMS

作　　者：马秀腾[1] 罗书强[1] 

机构地区：[1]西南大学工程技术学院,重庆400715

出　　处：《工程力学》2012年第12期40-44,共5页Engineering Mechanics

基　　金：中央高校基本科研业务费专项资金项目(XDJK2009C009);西南大学博士基金项目(SWU109048)

摘　　要：θ1方法是一种直接时间积分算法,主要用于结构动力学仿真时运动方程的求解,方程形式为二阶常微分方程(ODEs)。对于非完整系统动力学仿真,从微分-代数方程(DAEs)的角度看,系统的运动方程是二阶DAEs。基于此,提出非完整系统仿真的θ1方法,也就是数值求解指标-2的运动方程—DAEs的新算法。通过对双轮机器人θ1方法仿真结果与DASSL和Radau5算法结果的比较,验证新算法的有效性。数值实验也说明θ1方法求解非完整系统DAEs时具有2阶精度。The θ1 method is a direct-time integration method, which is used for the numerical integration of equations of motion in structural dynamics. The equations are second order ordinary differential equations （ODEs）. In the viewpoint of differential-algebraic equations （DAEs）, motion equations in non-holonomic systems are second order, too. Then θ1 method is extended and a new numerical method for the equations of motion in the non-holonomic systems is presented, while the equations are index-2 DAEs. The simulation for a two-wheeled robot by θ1 method is carried out, and the method is validated by comparing the solution with DASSL and Radau5. In addition, the numerical experiment also illustrates the second-order accuracy ofθ1method for DAEs in non-holonomic systems.

关 键 词：θ1方法 非完整系统 动力学仿真 微分-代数方程(DAEs) 2阶精度 

分 类 号：O313.7[理学—一般力学与力学基础]