Dynamics of Nonholonomic Systems from Variational Principles Embedded Variation Identity
Nondeterminacy of dynamics，I.e.，the nonholonomic or the vakonomic，fundamental variational principles，e.g. The Lagrange-d’Alembert or Hamiltonian，and variational operators，etc.，of nonholonomic mechanical systems can be attributed to the non-uniqueness of ways how to realize nonholonomic constraints. Making use of a variation identity of nonholonomic constraints embedded into the Hamilton’s principle with the method of Lagrange undermined multipliers，three kinds of dynamics for the nonholonomic systems including the vakonomic and nonholonomic ones and a new one are obtained if the variation is respectively reduced to three conditional variations: vakonomic variation，H¨older’s variation and Suslov’s variation，defined by the identity. Therefore，different dynamics of nonholonomic systems can be derived from an integral variational principle，utilizing one way of embedding constraints into the principle，with different variations. It is verified that the similar embedding of the identity into the Lagrange-d’Alembert principle gives rise to the nonholonomic dynamics but fails to give the vakonomic one unless the constraints are integrable.
非完整系统 变分原理 力学系统
Yong-Xin Guo Shi-Xing Liu
Physics College, Liaoning University, Shenyang 110036, China
国内会议
第十二届全国非线性振动暨第九届全国非线性动力学和运动稳定性学术会议
南京
英文
1-8
2009-05-15（万方平台首次上网日期，不代表论文的发表时间）