{"title":"中心力的嬗变和伯特兰定理","authors":"C. Carimalo","doi":"10.2298/tam220602001c","DOIUrl":null,"url":null,"abstract":"The transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand?s famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"14 9 Pt 1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Transmutation of central forces and Bertrand’s theorem\",\"authors\":\"C. Carimalo\",\"doi\":\"10.2298/tam220602001c\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand?s famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.\",\"PeriodicalId\":44059,\"journal\":{\"name\":\"Theoretical and Applied Mechanics\",\"volume\":\"14 9 Pt 1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/tam220602001c\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/tam220602001c","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Transmutation of central forces and Bertrand’s theorem
The transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand?s famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.
期刊介绍:
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