Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom

Pub Date : 2024-07-08 DOI:10.1134/s0012266124030042

M. V. Shamolin

引用次数: 0

Abstract

Tensor invariants (first integrals and differential forms) of homogeneous dynamical systems on the tangent bundles of smooth three-dimensional manifolds (systems with three degrees of freedom) are presented in this paper. The connection between the presence of such invariants and the complete set of the first integrals needed for the integration of geodesic, potential, and dissipative systems is shown. At the same time, the force fields introduced make the systems in question dissipative with dissipation of different signs and generalize the previously considered ones.

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具有三个自由度的大地、势和耗散系统的不变式

摘要本文介绍了光滑三维流形切线束上的均相动力系统（具有三个自由度的系统）的张量不变量（第一积分和微分形式）。本文说明了这些不变量的存在与测地、势和耗散系统积分所需的全套第一次积分之间的联系。同时，引入的力场使问题中的系统具有不同符号的耗散，并对之前考虑的系统进行了扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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