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

Tao Qing-sheng

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(12): 1097-1102

Tao Qing-sheng. A Tensor Method for the Derivation of the Equations of Rigid Body Dynamics[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1097-1102.

Citation:

Tao Qing-sheng. A Tensor Method for the Derivation of the Equations of Rigid Body Dynamics[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1097-1102.

Citation:

Tao Qing-sheng. A Tensor Method for the Derivation of the Equations of Rigid Body Dynamics[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1097-1102.

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

Tao Qing-sheng

Zhejiang University, Hangzhou

Received Date: 1990-10-15
Publish Date: 1991-12-15

Abstract

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.
- rigid body dynamics,
- dynamical equation,
- tensor

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References(14)

References

[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.