二阶非完整Vacco动力学及其Noether定理  

Second-order nonholonomic Vacco dynamics and its Noether's theorem

作　　者：张毅[1] ZHANG Yi(School of Civil Engineering,SUST,Suzhou 215011,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《苏州科技大学学报（自然科学版）》2023年第3期29-35,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(12272248,11972241)。

摘　　要：研究非完整约束Vacco动力学及其Noether对称性。建立二阶非完整系统的Vacco型变分原理,导出Vacco动力学方程。利用全变分与等时变分之间的关系,导出复合作用量的全变分公式。通过复合作用量在无限小变换下的不变性,定义Noether对称与准对称变换,给出对称性判据的Noether等式。建立二阶非完整约束Vacco动力学系统的Noether定理。如果约束是一阶非完整的,则定理退化为一阶非完整Vacco动力学的Noether定理。文末给出一个算例以演示定理之应用。Nonholonomic constrained Vacco dynamics and its Noether symmetry are studied.The Vacco type variational principle for second-order nonholonomic constrained system is established and the Vacco dynamical equations are derived.By using the relation between total variation and isochronous variation,the total variation formulas of compound action integral were derived.According to the invariance of composite action integral under infinitesimal transformation,the Noether symmetric and quasi-symmetric transformations were defined,and the Noether identities taken as symmetry criterion were given.Noether's theorem for Vacco dynamical system with second-order nonholonomic constraints was established.If the constraint is first-order nonholonomic,the theorem is reduced to Noether's theorem for first-order nonholonomic Vacco dynamics.Finally,an example was given to demonstrate the application of the theorem.

关 键 词：VACCO动力学 二阶非完整约束 NOETHER定理 守恒量 

分 类 号：O316[理学—一般力学与力学基础]