{"title":"Cases of Further Integrability of the Equation of Motion in the Presence of the Local Integral in the Space Model. I","authors":"F. T. Shamshiev","doi":"10.1134/S1990341323600308","DOIUrl":null,"url":null,"abstract":"<p>A local integral that allows us to immediately determine the velocity field for certain specific initial conditions was introduced by Antonov and Shamshiev in 1992. We consider cases where the integrability of the trajectory can be advanced further. We then obtain an analytical relationship between <span>\\(x\\)</span>, <span>\\(y\\)</span>, <span>\\(z\\)</span>, <span>\\(t\\)</span> on a given trajectory. Possible cases are classified and one of them is analyzed.</p>","PeriodicalId":478,"journal":{"name":"Astrophysical Bulletin","volume":"79 1","pages":"151 - 158"},"PeriodicalIF":1.3000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astrophysical Bulletin","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1990341323600308","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
A local integral that allows us to immediately determine the velocity field for certain specific initial conditions was introduced by Antonov and Shamshiev in 1992. We consider cases where the integrability of the trajectory can be advanced further. We then obtain an analytical relationship between \(x\), \(y\), \(z\), \(t\) on a given trajectory. Possible cases are classified and one of them is analyzed.
期刊介绍：
Astrophysical Bulletin is an international peer reviewed journal that publishes the results of original research in various areas of modern astronomy and astrophysics, including observational and theoretical astrophysics, physics of the Sun, radio astronomy, stellar astronomy, extragalactic astronomy, cosmology, and astronomy methods and instrumentation.
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