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

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.