Lagrange子流形理论在约束力学系统正则变换和勒让德变换中的应用  

APPLICATION OF LAGRANGE SUBMANIFOLD THEORY IN THE CANONICAL TRANSFORMATION AND LEGENDRE TRANSFORMATION OF CONSTRAINED MECHANICAL SYSTEMS

作　　者：刘畅[1,2] 王聪 刘世兴 郭永新[1] Liu Chang;Wang Cong;Liu Shixing;Guo Yongxin(College of Physics Liaoning University,Shenyang 110036,China;State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]辽宁大学物理学院,沈阳110036 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《动力学与控制学报》2019年第5期439-445,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11772144,11572145,11472124)~~

摘　　要：Lagrange方程与Hamilton方程之间的勒让德变换理论和Hamilton方程的正则变换理论在分析力学中具有重要的地位,从局域坐标的角度很难找到勒让德变换和正则变换之间的相关性.本文主要基于辛流形的Lagrange子流形理论从全局上给出正则变换理论和勒让德变换理论的统一几何解释,进而在几何力学的角度清晰的描述Hamilton系统的正则变换和Lagrange方程与Hamilton方程之间的勒让德变换的几何结构.Both the Legendre transformation between Lagrange′s equations and Hamilton′s equations and the ca nonical transformation theory of Hamilton′s equations play an important role in analytical mechanics.There seems to be no relationship between them from a local perspective.In this paper,based on the Lagrangian submanifold theory of symplectic manifold,the unified geometric interpretation of the canonical transformation theory and the Legendre transformation theory was given globally.Then,by utilizing geometric mechanics,the geometric struc ture of the canonical transformation for a Hamilton system and the geometric Legendre transformation between La grange′s equations and Hamilton′s equations were clearly described.

关 键 词：约束力学系统 Lagrange子流形 辛流形 正则变换 勒让德变换 

分 类 号：O41[理学—理论物理]