運動群とそのリー代数に基づく運動解析

概要

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For the purpose of establishing the mathematical beckground of a kinematic analysis of a multiple body system, the Lie aglebra of a motion group has been studied, and the algebraic experessions for kinematic analysis which is applicable any motion group is determined. Firstly it is shown that the equations for determining relative velocities and accelerations among rigid bodies can be expressed by the Lie algebra of addition and commutator product representing a Lie algebra of a motion group. Next, it is also clarified that the velocity and the acceleration of the point on a rigid body in a motion can be computed by multiplying an function of elements of the Lie algebra to the vector indicating the point from the left side. There exist eight groups of the rigid body motion, and the characteristics of the motin groups can be described by the theory of Lie algebra.
一般社団法人日本機械学会の論文
2000-06-25