第二类拉格朗日方程在无初速释放动力学问题中的应用

第二类拉格朗日方程在求解复杂动力学问题中有着广泛的应用,其特点是：只要求出系统在一般位置时的动能及相应于各广义坐标的广义力,经过程序化的求导运算就可获得控制系统的动力学方程。正是因为需要对系统的动能进行求导运算,第二类拉格朗日方程不能在系统的特殊位置求写系统的动能,而求写系统在一般位置时的动能很多情况下是一件不容易的事情,这正是应用拉格朗日方程的最大障碍。我们经过理论分析发现对无初速释放动力学问题,第二类拉格朗日方程提供了简便的求解途径。

THE APPLICATIONS OF LAGRANGE’S EQUATION FOR THE DYNAMIC PROBLEMS OF VELOCITY-FREE RELEASE

The Lagrange’s equation is widely used in solving complex dynamic problems. As soon as the kinetic energy of a system at a general position is known, the governing equation of the system can be easily obtained by the Lagrange’s equation. But to calculate the kinetic energy of a system at a general position is not easy in many cases, which is an obstacle to the application of the Lagrange’s equation. From a theoretical analysis, we find that to the dynamic problems of the velocity-free release, the Lagrange’s equation provides a simple way of solution.