非线性非完整系统Vacco动力学的积分理论

INTEGRATION THEORY FOR VACCO DYNAMICS OF NONLINEAR NONHOLONOMIC SYSTEMS

本文建立非线性非完整系统Vacco动力学方程的积分理论,由Vacco方程给出系统的第一积分,分别利用循环积分和能量积分降阶Vacco型方程,得到Vacco型广义Routh方程和广义Whittaker方程,建立了Vacco型正则方程和变分方程,并由第一积分构造系统的一类积分不变量,最后,给出其Poincare-Cartan型、Poincare型积分变量关系和积分不变量。

This paper studies integration theory for Vacco dynamical equation of nonlinear nonholonomic system. First, the first integrals of Vacco equation are given. Secondly, using cyclic integral and energy integral respectively, the order of Vacco equation is reduced, generalized Routh equation and generalized whittaker equation of Vacco form are obtained. Third, the canonical equation and variational equation of Vacco form are extended; by using a first integral, an integral invariant is construted. Finally, the basic integral variant and the integral invariant of Poincaré-Cartan form and Poincaré form for Vacco dynamics are given.