由欧拉角确定一次回转轴的简单解法  

A SIMPLE METHOD FOR DETERMINING THE EULER EIGENAXIS BY EULER ANGLES

作　　者：张媛 王士敏[1] 王琪[1] ZHANG Yuan;WANG Shimin;WANG Qi(Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学,北京100083

出　　处：《力学与实践》2022年第1期149-154,共6页Mechanics in Engineering

摘　　要：欧拉-达朗贝尔定理表明,定点运动刚体的有限位移可以通过绕一固定轴的一次转动实现。本文介绍了一种利用欧拉角求解刚体从任意一个姿态到另一个姿态作一次转动的转轴位置及回转角度的计算方法,给出了以欧拉角表示的一次回转轴公式。和求解坐标变换矩阵特征向量的方法比较,该算法计算量小,在应用上更为简便。As the Euler-d’Alembert theorem demonstrated,the finite displacement of a rigid body that rotates around a fixed point can be realized by rotating around the eigenaxis.This paper introduces a simple method for determining the eigenaxis and the corresponding rotational angle when a rigid body rotates from one attitude to another,it also provides the formula of calculating the direction of the eigenaxis by Euler angles.Compared with the way of solving the eigenvector of the coordinate matrix,the method proposed in this paper has lower computational complexity and is more convenient to use.

关 键 词：一次回转轴 一次回转角 欧拉-达朗贝尔定理 欧拉角 

分 类 号：O31[理学—一般力学与力学基础]