用第一类Lagrange方程求解平面多体系统约束力的方法

利用第一类Lagrange方程建立多体系统的动力学方程时,系统的约束力是与Lagrange乘子有关的函数。该文采用笛卡儿坐标和建立约束方程的局部方法,给出了一种求解多体系统约束力的方法。该方法可使固定支承面的法向约束力及铰链约束力在惯性坐标轴上的投影与Lagrange乘子一一对应,从而便于系统约束力的分析和求解,最后用算例验证了该方法的正确性。

A METHOD FOR SOLVING CONSTRAINED FORCE OF PLANAR MULTI-BODY SYSTEM VIA THE FIRST KIND OF LAGRANGE'S EQUATIONS

In the dynamic equations of multi-body system derivated by the first kind of Lagrange’s equations, the idealized constraint forces can be expressed as functions of the Lagrange multipliers. An approach to solve constraint forces of multi-body system is presented by means of Cartesian coordinate and partial approach of con- straint equations. The normal constraint force of fixed surface and the projection of each joint reaction force in in- ertia coordinate are related to Lagrange multipliers one-to-one, so that the constraint forces can be derived. A nu- merical example is used to demonstrate the effectiveness of this method.