{"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}
引用次数: 1
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.
期刊介绍:
Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.