# The theory of relativistic analytical mechanics of the rotational systems

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## 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\(T_r^* = \sum\limits_{i = 1}^n {I_{oi} \Gamma _i^2 (1 - \sqrt {1 - \dot \theta _i^2 /} \Gamma _i^2 )} \) and the generalized acceleration energy function\(S_r^* = \frac{1}{2}\sum\limits_{i = 1}^n {I_i \left[ {\frac{{(\theta _i \cdot\dot \theta _i )^2 }}{{\Gamma _i^2 - \dot \theta _i^2 }} + \dot \theta _i^2 } \right]} \) are constructed, and furthermore, 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; the relativistic Noether conservation law of the rotational systems are given too.

## Key words

rotational systems relativity analytical mechanics nonholonomic constraints variation principle equation of motion conservation law## Preview

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