推导刚体动力学方程的张量方法  

A Tensor Method for the Derivation of the Equations of Rigid Body Dynamics

作　　者：陶庆生[1] 

机构地区：[1]浙江大学力学系

出　　处：《应用数学和力学》1991年第12期1097-1102,共6页Applied Mathematics and Mechanics

摘　　要：本文提出了基于连续介质力学概念推导刚体动力学方程的张量方法,运用具有零共旋率的惯性张量的时间导数公式,证明了Lagrange方程、Nielsen方程、Gibbs-Appell方程、Kane方程和广义动量式Kane方程等五种方法的等价性,给出了角速度、角加速度之间的一些微分关系式.A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor -with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.

关 键 词：刚体动力学 动力学方程 张量 

分 类 号：O313.3[理学—一般力学与力学基础]