{"title":"Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom","authors":"M. V. Shamolin","doi":"10.1134/s0012266124030042","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Tensor invariants (first integrals and differential forms) of homogeneous dynamical systems\non the tangent bundles of smooth three-dimensional manifolds (systems with three degrees of\nfreedom) are presented in this paper. The connection between the presence of such invariants and\nthe complete set of the first integrals needed for the integration of geodesic, potential, and\ndissipative systems is shown. At the same time, the force fields introduced make the systems in\nquestion dissipative with dissipation of different signs and generalize the previously considered\nones.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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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