非线性非完整系统相对运动的第一积分与积分不变量

FIRST INTEGRALS AND INTEGRAL INVARIANTS FOR THE RELATIVE MOTION OF NONLINEAR NONHOLONOMIC SYSTEMS

本文给出了非线性非完整系统相对于非惯性系的循环积分和能量积分存在的条件,建立了这类系统的正则方程和变分方程,证明了系统的第一积分可以直接构造其积分不变量,并给出一系列推论。

The first integrals and their conditi on of existence for nonlinear nonholonomic system in onninertial refence frame are given, and the canonical equations and the variational equations of the system are extended. Using the first integral the construction of the integral invariants is proved. Finally, a series of deductions aregiven.