摘要
本文讨论了转动相对论力学理论，主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Ｔｒ＝∑ｎｉ＝１Ｉ０ｉΓｉ２（１－１－θ·２ｉ／Γｉ２）和广义加速度能量函数Ｓｒ＝１２∑ｎｉ＝１Ｉｉ（θ·ｉ·θ¨ｉ）２Γｉ２－θ·２ｉ＋θ¨２ｉ，给出其Ｈａｍｉｌｔｏｎ原理和三种不同形式的Ｄ′Ａｌｅｍｂｅｒｔ原理；对于完整约束系统，建立了转动系统的相对论性Ｌａｇｒａｎｇｅ方程、Ｎｉｅｌｓｅｎ方程、Ａｐｐｅｌ方程和Ｈａｍｉｌｔｏｎ正则方程；对于非完整约束系统，建立了转动系统的相对论性Ｒｏｕｔｈ方程、Чаплыгин方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌ方程；
The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics of the rotational systems is constructed.The relativistic generalized kinetic energy function for the rotational systems T*r=∑ni=1IoiΓ2i1-1-θ·2i/Γ2i and the generalized acceleration energy function S*r=12∑ni=1Ii(θ·i·θ¨i)2Γ2i-θ·2i+θ¨2i are constructed and further,the Hamilton principle and three kinds of D′Alembert principles are given.For the systems with holonomic constraints,the relativistic Lagrange equation,Nielsen equation,Appell equation and Hamilton canonical equation of the rotational systems are constructed;For the systems with nonholonomic constraints,the relativistic Routh equation,Chaplygin equation,Nielsen equation and Appell equation of the rotational systems are constructed;and the relativistic Noether conservation law of the rotational systems are given too.
出处
《应用数学和力学》
CSCD
北大核心
1998年第1期43-53,共11页
Applied Mathematics and Mechanics
基金
河南省自然科学基金
关键词
转动系统
相对论
分析力学
非完整约束
变分原理
rotational systems,relativity,analytical mechanics,nonholonomic constraints,variation principle,equation of motion,conservation law
