关于分析力学中约束力的表达问题

本文针对分析力学中约束力表达式是否合理的问题，分析了约束、约束方程、约束力、位移和运动学限制等概念之间的关系并建议了一个新的关系，指出：（１）即使是理想约束，约束力也只能由约束而不是由约束方程统一确定；（２）实现运动学限誓由蝗途径不是唯一的，约束力的乘子表达式不是普遍适用的。给出了对于具体的约束，约束力表达式正确与否的判别原则。示例说明了上述论点。

ON THE EXPRESSIONS OF CONSTRAINT FORCES IN ANALYTICAL DYNAMICS

In this paper, in order to show the expressions of constraint forces in analytical dynamics are resonable or not, the relationships between the concepts of constraints, constraint equations, constraint forces, virtual displacements and constraints in kinematics are analysed and a new relationships between them are suggested. It is pointed out that frist. the expressions of constraint forces can only be determined by the constraint instead of the constraint equations, second, the way to realize the constraint in kinematics is not unique, and the expressions of constraint forces with multipliers are not always reasonable in general cases. A method to judge whether the expression of constraint force is reasonable or not is given. An example is discussed to illustrate the above viewpoints.