受冲击性约束作用的系统的运动方程
The Equations of Motion of a System under the Action of the Impulsive Constraints
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摘要: 当具有n个自由度的系统加有P个冲击性的约束时,要求解系统的运动,一般都需要解含n+P个方程的方程组.本文提出以待定乘子法为基础,分别就取广义坐标和伪坐标的二种情况,从n个碰撞方程中消去未知的待定乘子,将碰撞方程简化为n-P个,它和P个冲击性约束方程一起组成了含n个方程的方程组,就能求解具有冲击性约束的碰撞问题,这比一般方法更为简便.Abstract: In order to solve the problem of motion for the system with n degrees of freedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting ofn equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.
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[1] 汪家訸,《分析力学》,高等教育出版社(1982,9). [2] 吴镇,《分析力学》,上海交通大学出版社(1984,9). [3] Greenwood,Donald T.,Classical Dynayraics,Prentice-Hall,Inc,(1977). [4] 张文,伪速度下的碰撞方程及其矩阵解法,固沐力学学报,4(1983). [5] 吉洪诺夫A,H.,A,A,萨马尔斯基,《数学物理方程》(上册),高等教育出版社(1953). [6] 孙右烈,受冲力作用的非完整系统的运动方程,应用数学和力学,8,2(1987),169-176 [7] 甘特马赫Ф.P.《分析力学讲义》,人民教育出版社(1963).
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