## 留言板

 引用本文: 陶庆生. 推导刚体动力学方程的张量方法[J]. 应用数学和力学, 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.

## 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.
•  [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.
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##### 出版历程
• 收稿日期:  1990-10-15
• 刊出日期:  1991-12-15

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