Invariants of Systems Having a Small Number of Degrees of Freedom with Dissipation

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2024-07-29 DOI:10.3103/s0027132224700116

M. V. Shamolin

引用次数: 0

Abstract

Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles to smooth two-dimensional manifolds are presented in the paper. The connection between the presence of these invariants and the full set of first integrals necessary for integration of geodesic, potential, and dissipative systems is shown. At the same time, the introduced force fields make the considered systems dissipative with dissipation of different signs and generalize the previously considered ones. We represent the typical examples from rigid body dynamics.

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带有耗散的少量自由度系统的不变式

摘要本文提出了光滑二维流形切线束上的均相动力系统的张量不变量（微分形式）。文中指出了这些不变量的存在与测地、势和耗散系统集成所需的全套第一积分之间的联系。同时，引入的力场使得所考虑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。我们用刚体动力学中的典型例子来说明这一点。

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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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.