引用本文: 王睿垠, 袁威, 冯放等. 刚体动量矩和动能的一般表示. 力学与实践, xxxx, x(x): 1-5.
Wang Ruiyin, Yuan Wei, Feng Fang, et al. The general expressions for angular momentum and kinetic energy of rigid body. Mechanics in Engineering, xxxx, x(x): 1-5.
 Citation: Wang Ruiyin, Yuan Wei, Feng Fang, et al. The general expressions for angular momentum and kinetic energy of rigid body. Mechanics in Engineering, xxxx, x(x): 1-5.

## THE GENERAL EXPRESSIONS FOR ANGULAR MOMENTUM AND KINETIC ENERGY OF RIGID BODY

• 摘要: 本文研究了平面运动刚体，在选择任意点为基点时，对该点的动量矩和动能的一般表达式。同时，针对复杂的多体问题，将动能的一般形式推广到广义质量和广义速度乘积的矩阵形式，通过多体系统的第一个刚体，递归生成多个铰接的刚体的广义速度，并利用动能的矩阵形式来给出多体系统的动能。通过比较以质心为基点和采用矩阵形式两种计算动能的过程，说明了可以应用矩阵形式统一给出多体系统的动能。

Abstract: This paper studies the planar motion of rigid body and provides a general expression for the angular momentum and kinetic energy with respect to an arbitrary point. Moreover, for multiple rigid bodies, this paper extends the kinetic energy to matrix form of generalized mass and generalized velocity products. By recursively generating the generalized velocities of articulated bodies through the first rigid body, the kinetic energy of the multiple rigid bodies is derived using the matrix form. Comparing the calculation processes of kinetic energy using the center of mass as the reference point and those using the matrix form, it explains that the matrix form can be universally employed to expressed the kinetic energy of multibody systems.

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