从Lagrange方程导出刚体动力学的Euler方程  

Euler's Equation of Rigid Body Dynamics Derived from Lagrange's Equation

作　　者：薛纭[1] 沈洁 

机构地区：[1]上海应用技术学院机械与自动化工程学院,上海200235 [2]上海市泾南中学,上海200135

出　　处：《上海应用技术学院学报（自然科学版）》2008年第3期157-159,共3页Journal of Shanghai Institute of Technology: Natural Science

基　　金：国家自然科学基金资助项目(10472067)

摘　　要：从Lagrange方程推导定点转动刚体的Euler方程要借助刚体的姿态角。刚体的角速度用主轴基及其导数表示,表明了其Boltzmann三标记号的值与广义坐标的具体形式无关,据此,在不涉及广义坐标具体形式的前提下,从完整系统的Lagrange方程出发导出刚体动力学的Euler方程。It is known to all that Euler＇s equation of rigid body dynamics may be easily derived from Lagrange Equation by means of Euler angles of the body. It is proved that the values of Boltzmann three-index symbols are independent of the choice of generalized coordinates of the body, （expressing the angular velocity of the body in terms of its principal basis and their derivative with respective to the time. ） Based on this factor, Euler equation of rigid body dynamics is derived from Lagrange equation with no Euler angles.

关 键 词：刚体动力学 EULER方程 LAGRANGE方程 广义坐标 

分 类 号：O313.3[理学—一般力学与力学基础]