转动系统的相对论性分析力学理论*
The Theory of Relativistic Analytical Mechanics of the Rotational Systems
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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*= 和广义加速度能量函数Sr*=,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;并给出转动系统的相对论性Noether守恒律.Abstract: 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 Tr*= and the generalized acceleration energy function Sr*= are constructed and further, the Hamilton 27 principle and three kinds of Dc 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
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