关于刚体惯量矩阵的两个问题

Two Problems about Inertia Matrices of Rigid Bodies

本文阐述了刚体对于平行的质心坐标系与非质心坐标系的惯量矩阵间的关系,推导了一个公式,并给出了惯量张量在不同坐标系中的坐标矩阵间的变换规则,从而可以计算刚体在任一坐标系中的惯量矩阵。文章叙述了确定刚体在某点的惯性主轴与主惯性矩问题可以转化为求惯量矩阵的特征值问题,说明了具体解法与有关量的意义,最后给出一个算例。

The relationship between two inertia matrices of a rigid body is discussed with respect to two parallel reference frames… the centre of mass coordinate system and the non-centre of mass coordinate system. A relevant formula is developed and a transformation equation is offered for the coordinate matrices of an inertia tensor between the two systems, by using which the inertia matrix of a rigid body in either system can be obtained. Problems of determining principal axes and principal moments of inertia for a rigid body with respect to a certain reference point can be transformed into problems about the eigenvalues for the inertia matrices. The method itself and the significance of the relevant parameters are illustrated in detail. Lastly, an example is povided