摘要
研究了运动约束面含摩擦多体系统动力学方程的建立和算法问题。首先利用第一类Lagrange方程给出了系统的动力学方程,并以矩阵形式给出了这类系统摩擦力的广义力的一般表达式。为便于摩擦力和铰链约束力的分析与计算,采用笛卡尔坐标和约束方程的局部方法,使得系统的约束力与Lagrange乘子一一对应。应用增广法将微分-代数方程组转化为常微分方程组并用分块矩阵的形式给出,以便于方程的编程与计算,提高计算效率。最后用一个算例验证了该方法的有效性。
A method for dynamics modeling and numerical algorithm of multi-body system with friction and Moving-bilateral-Slot was provided. At first, the dynamic equations of the system were derived from the first kind of Lagrange＇ s equations by using the Cartesian coordinates and local approach of constraint equations. A one-to-one correspondence between the constraint forces of the system and the Lagrange multipliers was established to analyze and compute the friction forces conveniently. Secondly, with the augmentation approach, the differential-algebraic equations were transformed into ordinary differential equations of partitioned matrix form, which can improve the calculating efficiency. Finally, a numerical example was given to prove the method to be effective.
出处
《动力学与控制学报》
2009年第2期113-118,共6页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(10672007)~~
关键词
多体系统
双面约束
LAGRANGE乘子
干摩擦
multi-body system, bilateral constraint, multiplier of Lagrange, dry friction
