{"title":"论Ricatti微分方程在变质量两体问题某些特殊情况下的应用","authors":"Ilhan M. Izmirli","doi":"10.12691/AJAMS-9-2-3","DOIUrl":null,"url":null,"abstract":"In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"81 1","pages":"53-56"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Applications of Ricatti Differential Equations to Some Special Cases of the Two-Body Problem with Variable Masses\",\"authors\":\"Ilhan M. Izmirli\",\"doi\":\"10.12691/AJAMS-9-2-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions.\",\"PeriodicalId\":91196,\"journal\":{\"name\":\"American journal of applied mathematics and statistics\",\"volume\":\"81 1\",\"pages\":\"53-56\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American journal of applied mathematics and statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12691/AJAMS-9-2-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American journal of applied mathematics and statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12691/AJAMS-9-2-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Applications of Ricatti Differential Equations to Some Special Cases of the Two-Body Problem with Variable Masses
In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions.
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