旋量理论及其在理论力学中的应用

TORSEUR THEORY AND ITS APPLICATION IN THEORETICAL MECHANICS

旋量理论是为力学量身定制的数学工具,因其力学描述统一性,数学描述一般性和计算“求解过程”程式化,在对“多刚体”动力学问题“建模、分析和求解”时具有独特的优势:一方面借助螺旋量将刚体的平移和转动描述进行统一;另一方面从数学上进行严谨论述的同时引出对应的物理概念,使得数学性质和物理意义能得到相互映照。本文简要阐述了旋量理论目前在国内外力学教学中的研究现状;介绍了旋量的数学定义及其满足的数学运算性质;梳理了理论力学中的四种基本螺旋量,并给出了矢量静力学和动力学“基本定理”的旋量描述。希望通过本文的研究能为我国理论力学教学提供启示。

Torseur theory is a mathematical tool specially designed for mechanics.Thanks to its unified mechanical description,mathematical generality and operational simplicity,it has significant advantages in modeling,analyzing and computing rigid multibody dynamics:on the one hand,unifying the translation and rotation process in the same mathematical notation;one the other hand,establishing correct physical concepts while making strict mathematical expositions,so that mathematical properties and physical meanings can be well reflected on each other.This paper briefly introduces the research status of spiral theory in mechanics teaching in China and abroad.The mathematical definition of torseur and its mathematical operation properties are presented.The four basic spirals commonly used in theoretical mechanics are expounded,and the spiral descriptions of“fundamental theorems”of vector statics and dynamics are formulated.It is expected that this study can provide new ideas for theoretical mechanics teaching in China.