高阶非完整约束系统嵌入变分恒等式的积分变分原理

The integral variational principles for embedded variation identity of high-order nonholonomic constrained systems

本文从高阶非完整系统嵌入变分恒等式的积分变分原理出发,根据三种不等价条件变分的选取,得到了高阶非完整系统的三类不等价动力学模型,即高阶非完整约束系统的vakonomic方程、Lagrange-d’Alembert方程和一种新的动力学方程.当高阶非完整约束方程退化为一阶非完整约束时,利用此理论可以得到一般非完整系统的vakonomic模型、Chetaev模型和一种新的动力学模型.最后借助于应用实例验证了结论的正确性.

In this article, from the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems, three kinds of dynamics for high-order nonholonomic constrained systems are obtained, including the vakonomic dynamical model, Lagrange-d’Alembert model and a new one if utilizing respectively three kinds of conditional variation to them. And the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems is also fitted for the general nonholonomic systems when the constrained equation is reduced to a first-order one. Then, the vakonomic dynamic, Chetaev dynamics and a new model of general nonholonomic systems can also be obtained. Finally, two illustrated examples are used to verify the validity of the theory.