{"title":"Generalized Non-Standard Lagrangians","authors":"N. Davachi, Z. Musielak","doi":"10.1063/1.5129244","DOIUrl":null,"url":null,"abstract":"A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129244","citationCount":"14","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of undergraduate reports in physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5129244","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 14
Abstract
A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.
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