Applied Mathematics and Mechanics (English Edition) ›› 1991, Vol. 12 ›› Issue (12): 1163-1168.

• 论文 • 上一篇    下一篇

A TENSOR METHOD FOR THE DERIVATION OF THE EQUATIONS OF RIGID BODY DYNAMICS

陶庆生   

  1. Zhejiang University, Hangzhou
  • 收稿日期:1990-10-15 出版日期:1991-12-18 发布日期:1991-12-18
  • 通讯作者: Guo Zhong-heng

A TENSOR METHOD FOR THE DERIVATION OF THE EQUATIONS OF RIGID BODY DYNAMICS

Tao Qing-sheng   

  1. Zhejiang University, Hangzhou
  • Received:1990-10-15 Online:1991-12-18 Published:1991-12-18

摘要: 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: rigid body dynamics, dynamical equation, tensor

Abstract: 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.

Key words: rigid body dynamics, dynamical equation, tensor

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