PoincarU-Chetaev变量下变质量非完整动力学系统的运动方程

摘要

The equations of motion of variable-mass nonlinear nonholonomic dynamical systems in Poincaré-Chetaev variables have been studied. Firstly, the Poincaré-Chetaev variables x1,x2,…,xn and more with n-m holonomic constraints and m-l nonlinear nonholonomic constraints of Chetaev type were introduced. Secondly, the equations of Chaplygin's form, Nielsen's form and Appell's form were derived from the D'Alembert-Lagrange principle for a variable-mass mechanical system. Finally, the problem of equivalence between the Chaplygin's equations and the Appell's equations was discussed. Then the theory is illustrated by an example due to Appell.%研究Poincaré-Chetaev变量下，变质量非线性非完整力学系统的运动方程.首先，由变质量力学系统的D'Alembert-Lagrange原理导出Chaplygin型方程、Nielsen型方程及Appell型方程．其次，研究Chaplygin方程与Appell方程的等价性问题.最后，举例说明新结果的应用.