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
-
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.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
-
[1] Marsden,E.and T.J.R.Hughes,Mathematical Foundations of Elasticity,Prentice-Hall,Inc.(1983). [2] Guo Zhong-heng,Time derivatives of tensor fields in nonlinear continuum mechanics,Arch.Mech.Stosowanej,1,15(1963),131-163. [3] Hughes,T.J.R.,Numerical implementation of constitutive models:rate-independent deviatoric plasticity,Workshop on Theoretical Foundations for Large-Scale Computations of Nonlinear Material Behavior,Northwestern University,Evanston,IL.,USA(1983). [4] 需凡中,《弹塑性有限变形理论和有限元方法》,清华大学出版社(1985) [5] Truesdell,C.and R.A.Toupin,The Classical Field Theories Handbuch der Physik,Bd Ⅲ/1,Springer(1960). [6] Casey,J.,A treatment of rigid body dynamics,J.Appl.Mech.,50(1983),905-907. [7] 汪家訸,《分析力学》.高等教育出版社(1982). [8] Kane,T.R.,Dynamics,3rd.ed.,Stanford University,Stanford,California,USA(1978). [9] Kane,T.R.and D.A.Levinson,formulation of equations of motions for complex spacecraft,J.Guidance and Control,3,2(1980),99-112. [10] 梅凤翔.《非完整系统力学基础》,北京工业学院出版社(1985). [11] 陶庆生,新型广义动量式动力学方程,浙江大学学报,23(3)(1989),450-458 [12] Truesdell,C.,A First Course in Rational Continuum Mechanics,Vol.1,Academic Press(1977). [13] 梁昆淼.嘴力学多(下册),人民教育出版社(1980). [14] 梅凤翔,分析力学中的Nielsen算子和Euler算子,力学学报,16(6)(1984),596-603.
点击查看大图
计量
- 文章访问数: 2543
- HTML全文浏览量: 116
- PDF下载量: 489
- 被引次数: 0