用第一类Lagrange方程求解平面多体系统约束力的方法

详细信息

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

(School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China)

摘要: 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。
- 多体系统 /
- 理想约束 /
- 建模 /
- 约束方程 /
- Lagrange乘子
Abstract: In the dynamic equations of multi-body system derivated by the first kind of Lagrange’s equa¬tions, the idealized constraint forces can be expressed as functions of the Lagrange multipliers. An approach to solve con¬straint forces of multi-body system is presented by means of Cartesian coordinate and partial ap¬proach of constraint equations. The normal constraint force of fixed surface and the projection of each joint reac¬tion force in inertia coordinate are related to Lagrange multipliers one-to-one, so that the constraint forces can be derived. A numerical example is used to demonstrate the effectiveness of this method.
- multi-body system /
- idealized constraint /
- modeling /
- constraint equation /
- Lagrange multiplier