惯量张量及其特征值问题

THE PROBLEM OF INERTIA TENSOR AND ITS EIGEN VALUE

本交给出了惯量张量用其三个主要不变量表示的特征方程,为求特征值提供了一种代数方程解法;论证了特征值即为主惯量,特征矢量即为惯量主轴;探讨了用特征矩阵的伴随矩阵求惯量主轴的方法,并用实例给予了说明。

This paper presents the eigen equation of inertial tensor expressed by the three principal invariants, which is an algebra-equation solution to calculate eigen value;proves that eigenvalue is the principal moments of inertia and that eigenvector is the principal axes of inertia;and discusses a certain method to calculate prinpal axes of inertia by adjoint matrix of eigen matrix.Finally the paper explains this method by two concrete examples.