摘要
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.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2013年第9期315-320,共6页
Acta Physica Sinica
基金
国家自然科学基金(批准号:11202090
11172120
10932002)
辽宁省重点实验室建设项目(批准号:2008403009)资助的课题~~