广义第二类拉格朗日方程及其对非完整力学系统的应用

GENERALIZED LAGRANGE'S EQUATION OF THE SECOND KIND AND ITS APPLICATION IN NONHOLONOMIC SYSTEMS OF ANALYTICAL DYNAMICS

对于理想约束，按照广义理想约束力是否为零，把理想约束分为完全理想约束和不完全理想约束．对于一个物理模型确定的有约束力学系统，解除其实现运动约束的物理条件，代之以相应的约束力，这样就无须考虑运动约束加在虚位移上的限制条件，而建立起含有广义不完全理想约束力的广义第二类拉格日朗方程，并考虑到运动约束方程，就构成了该约束系统的封闭动力学方程组．

Ideal constraint can be divided into complete ideal constraint or incomplete ideal constraint according as generalized ideal constraint forces equal to zero or not. When a constrained mechanical system determined by physical models is relieved from physical conditions which implement the constraint of motion, and provided with the corresponding constraint forces instead, and then Generalized lagrange's equation of the second kind with generalized incomplete ideal constraint is established, not having to consider the restriction of placing constraints on virtual displacement. Further, in view of the constraint equation of motion, the closed dynamical equations for such constrained system can be established.