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.
作者
刘畅
王聪
刘世兴
郭永新
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)
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)~~
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
constrained mechanical systems
Lagrangian submanifold
symplectic manifold
canonical transformation
Legendre transformation
