时间尺度上完整非保守力学系统的Noether定理  

Noether’s theorem for holonomic nonconservative mechanical systems on time scales

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）》2020年第1期6-11,共6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(11972241,11572212);江苏省自然科学基金资助项目(BK20191454)。

摘　　要：研究时间尺度上完整非保守力学系统的Noether对称性与守恒量。给出时间尺度上Hamilton原理及其对非保守系统的推广,导出时间尺度上完整非保守力学系统的Lagrange方程。给出时间尺度上完整非保守力学系统的Noether对称性的判据和广义Noether等式。建立并证明时间尺度上非保守力学系统的Noether定理,揭示时间尺度上Noether对称性与守恒量之间的内在联系。如果不存在非保守力,则结果退化为时间尺度上Lagrange系统的Noether定理;如果时间尺度取为实数集,则结果退化为经典一般完整系统的Noether定理。文末给出一个算例以说明结果的应用。This paper studies the Noether symmetry and conserved quantity of a holonomic nonconservative mechanical system on time scales.The Hamilton principle on time scales and its extension to nonconservative system are given,and the Lagrange equations of a holonomic nonconservative mechanical system on time scales are derived.The criterion of Noether symmetry and the generalized Noether identity for the holonomic nonconservative mechanical system on time scales are given.Noether’s theorem for the nonconservative mechanical system on time scales is established and proved.The theorem reveals the internal relation between the Noether symmetry and the conserved quantity on time scales.If there is no nonconservative force,the result is reduced to Noether’s theorem of Lagrangian system on time scales.If the time scale is taken as a set of real numbers,the result is reduced to Noether’s theorem of the classical general holonomic system.Finally,the application of the results is illustrated.

关 键 词：非保守力学系统 时间尺度 NOETHER对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]