求解一类特殊力学量的特征矩阵对角化方法

在力学中有一类量的求解可归结为矩阵特征值和特征向量的求解 ,而求解矩阵的特征值将要求解高次方程的根 ,这在数学上将遇到难以克服的困难。本文把这类形式上相似的力学量用矩阵写成一个统一的表达式 ,并对这统一的表达式进行了讨论 ,揭示了各不同力学量本质的东西 ,给出了求解这类特殊的力学量的特征矩阵对角化方法。利用这种方法 ,同时可求出该矩阵所有的特征值和正交的特征向量 ,避免了求解高次方程根的困难与把各特征向量正交化的麻烦。

An Eigen-matrix Diagonalization Method for Solving A Category of Special Mechanical Quantities

In mechanics,solutions of some quantities may be achieved by solving eigen values and eigen vectors of matrix. However, to solve eigen values of matrix needs to solve roots of higher degree equation,which may encounter great difficulities .In this paper, the mechanical quantities with similar forms are written as a uniform matrix expression, which is futher discussed in the paper. Their essential aspect of these different mechanical quantities are revealed. An eigen matrix diagonalization method for solving this category of special mechanical quantities is derived. All the eigen values of the matrix and orthogonal eigen vectors can be solved by this method without solving higher degree equation and orthogonalization of every eigen vectors.