理论力学教学中点的运动合成定理的复空间阐述  

Complex number description about theorems on velocity and acceleration composition of a point mass

作　　者：牛聪民[1] NIU Cong-min(School of Mechanical and Electrical Engineering,Xiamen University Tan Kah Kee College,Zhangzhou 363105,China)

机构地区：[1]厦门大学嘉庚学院机电工程学院,福建漳州363105

出　　处：《武汉轻工大学学报》2020年第1期111-114,118,共5页Journal of Wuhan Polytechnic University

基　　金：福建省教学改革重大项目(FBJG20180093)。

摘　　要：由于理论力学教材之点的运动合成定理中相对位移、相对速度、相对加速度等概念内涵的不完整,使这些看似简单的运动学规律成了课程教学实践的难点和争论点。应用复分析理论论证后发现:定理中的相对位移、相对速度和相对加速度等概念与教材中定义的概念(动系中观察者观测到的位移、速度和加速度)并非同一概念,而分别是定义在定系和动系中的、具有确定映射关系的两类概念。通过复空间阐述,彻底分清了上述两类概念,使点的运动合成定理得到准确表述。Because of incomplete connotations of relative displacement,velocity and acceleration defined in theorems on velocity and acceleration composition of a point mass in textbooks,these theorems have always been a teaching difficulty and argument.After analysis and demonstration by applying complex analysis theory,it is found that the relative velocity,acceleration and displacement described in theorems are not the same concepts as the ones measured by an observer in a moving reference frame.In fact they belong to two kinds of concepts defined in different reference frames,a fixed frame and a moving frame respectively,and have a determined mapping relationship each other.Though complex number expressions,not only can the above two kinds of concepts be distinguished fully,but also theorems on velocity and acceleration composition of a point mass can be described exactly.

关 键 词：点的运动合成定理 复分析法 映射 相对位移 相对速度 相对加速度 

分 类 号：O311[理学—一般力学与力学基础]