一种利用矩阵变换定位刚体惯量主轴的方法  

A Method Using Matrix Transformation to Position the Principal Axis of Inertia of Rigid Bodies

作　　者：贾伟尧[1] 邹愉[1] 邹新政[1] 张巧明[1] 

机构地区：[1]西南大学物理科学与技术学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2016年第1期173-178,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：西南大学网络与继续教育教学研究基金项目(wj2014016);国家自然科学基金青年基金项目(11404266)

摘　　要：针对理论力学教材中对惯量张量讨论甚少,学生不易理解的问题,通过矩阵运算法则,对几个常见刚体模型相对于任意点为坐标原点的惯量张量进行对角化.找出了矩阵变换与刚体定点转动的对应关系,给出了一种通过惯量矩阵确定惯量主轴的方法.该方法适用于任意形状的刚体,可以在教学中增强学生对惯量张量物理思想的理解并激发学生的学习兴趣.Taking into consideration the fact that the problem of tensor of inertia is little discussed in the teaching materials of theoretical mechanics and the students find it difficult to understand,we diagonalize,in this paper,the tensor of inertia of several common rigid bodies based on any-point through matrix algorithm.We also discover the corresponding relation between matrix transformation and fixed point rotation of rigid bodies.We propose a physical idea on the confirmation of the principal axis of inertia.This idea is suitable for the rigid bodies with any shape and can also help students to understand the physical thought of tensor of inertia and consequently motivate them to learn it.

关 键 词：惯量积 惯量主轴 矩阵对角化 刚体转动 

分 类 号：G642.0[文化科学—高等教育学]