物理与工程

张量是理论物理中非常重要的一个概念。转动惯量张量是本科课程中学生第一次接触张量这个概念。本文尝试通过对转动惯量张量教学内容的创新,对刚体转动惯量张量的教学内容进行重新编排,先计算刚体定点转动角动量,再引入矩阵形式,最后引进转动惯量张量、并矢的概念及其计算规则。让学生理解张量的引入是自然而然的,只是对问题描述数学形式的一种,但能带来方便。以此为切入点,为学生后续学习包含张量的理论打下坚实的基础,同时培养学生的创新思维。

Tensors are a very important concept in theoretical physics. The inertia tensor is the first concept of tensors that students encounter in undergraduate courses. This paper attempts to innovate the teaching content of the inertia tensor by reorganizing the teaching content of the inertia tensor of rigid bodies. It starts with calculating the angular momentum of a rigid body rotating about a fixed point, then introduces the matrix form, and finally introduces the concept of the inertia tensor, dyadic notation, and their calculation rules. This approach helps students understand that the introduction of tensors is natural and is just a mathematical form of problem description, but it brings convenience. Using this as a starting point, it lays a solid foundation for students' subsequent learning of theories involving tensors and also cultivates their innovative thinking.