拉梅系数在力学中的应用  

Some applications of Lame coefficient in mechanics

作　　者：周健 马瑛晗 毛英臣[1] ZHOU Jian;MA Ying-han;MAO Ying-chen(School of Physics and Electronic Techology,Liaoning Normal University,Dalian Liaoning 116029,China)

机构地区：[1]辽宁师范大学物理与电子技术学院,辽宁大连116029

出　　处：《大学物理》2022年第8期26-29,共4页College Physics

基　　金：2020年辽宁省教育厅科学研究项目(LF2020002);2021年度高等学校理论力学课程教学研究项目(JZW-21-LL-05)资助。

摘　　要：从拉梅系数的定义出发,计算了常用的正交曲线坐标系的拉梅系数,并给出了利用拉梅系数表示的线元、面元和体元.结合具体问题,讨论了拉梅系数在运动学和分析力学中的应用,通过分析可知拉梅系数揭示了一类物理问题的数学基础,利用拉梅系数有助于简化对该类问题的理解,减少计算步骤.此外,利用拉梅系数还有利于对力学知识串联整合.Based on the definition of Lame coefficient, this paper calculates the Lame coefficients in the commonly used orthogonal curvilinear coordinate systems, and gives the arc length, panel element and volume element represented by Lame coefficient. Combined with specific problems, the application of Lame coefficient in kinematics and analytical mechanics is discussed. Through analysis, it can be seen that the Lame coefficient reveals the mathematical basis of one kind of physical problems, which is conducive to simplifying the understanding of this kind of problems and reducing the calculation steps. Furthermore, the use of the Lamé coefficient promotes the integration of related mechanics knowledge.

关 键 词：拉梅系数 广义力 虚功原理 动能函数 

分 类 号：O31[理学—一般力学与力学基础]