受冲力作用的非完整系统的运动方程
The Equations of Motion for a Nonholonomic System under the Action of.lmpulsive Forces
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摘要: 有关用广义坐标表示的非完整系统的碰撞方程组,在一般分析力学著作中已有详细的叙述,但在这些方程中,都包含有待定乘子,这些未知量的出现使问题变得复杂.本文通过适当的数学处理,推出了用广义坐标表示的、不含待定乘子的非完整系统的碰撞方程组,简化了问题.由于运用了δ函数以及矩阵表示,因而使推导与结论更简洁明瞭.Abstract: The equations of impact for a nonholonomic system described with generalized coordinated have been discussed in detail in the general references of classical dynamics. But these equations contain undetermined multipliers which made the problem complicated.Through the appropriate treatment of mathematics, using the 8 -function and expression of matrix in this paper, the author derived equations of impact for a nonholonomic system without undetermined multipliers. Therefore, the problem can be solved more simply.
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[1] 汪家泳,《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(1984,9). [3] Greenwood,Donald T.,Classical Dynamics,Prentice-Hall,Inc.(1977). [4] 甘特马赫,Φ.P.《分析力学讲义》,人民教育出版社(1961). [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(1960). -
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