非线性非完整空间变质量体的一种运动方程*
The Equation of Motion for the System of the Variable Mass in the Non-Linear Non-Holonomic Space
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摘要: 引入非线性非完整空间的约束超曲面的基矢量和密歇尔斯基方程点乘,作为非线性非完整系统变质量体的基本动力学方程。它简明、运算简便,而且由它可导出,Nielsou,Appell,Mac-Millan等已有的方程,不必附加关于虚位移的Appell-定义或牛青萍定义。本方程与D'Alembert-Lagrange微分变分原理相容。Abstract: The dot product of bases vectors on the super-surface of constraints of the nonlinear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable mass.These are very simple and convenient for computation.From these known equations,the equations of Chaplygin,Nielson,Appell,Mac-Millan et al.are derivd,it is unnecessary to introduce the definition if Appell-Chetaev or Niu Qinping for the virtual displacement.These are compatible with the D'Alembert-Lagrange's principle.
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[1] 梅凤翔,《非完整系统力学基础》,北京工业学院出版社,北京(1985),403-405, [2] 郭仲衡、高普云,关于经典非完整力学,力学学报.22(2)(1990),185, [3] 高普云、郭仲衡,一类非完整力学系统的Lagrange方程,应用数学和力学,12(5)(1991),397-400, [4] 陈滨,关于经典非完整力学的一个争议,力学学报,23(3)(1991),379, [5] 郭仲衡、高普云,再论关于非完整力学—答《争议》.力学学报,24(2)(1992),253, [6] 梅凤翔,《非完整动力学研究》,北京工业学院出版社,北京,(1987),148-149, -
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