{"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":50580,"journal":{"name":"Differential Equations","volume":"31 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030042","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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