{"title":"椭圆运动的规范处理","authors":"Ola A. Jarab’ah","doi":"10.4236/apm.2023.139041","DOIUrl":null,"url":null,"abstract":"The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Canonical Treatment of Elliptical Motion\",\"authors\":\"Ola A. Jarab’ah\",\"doi\":\"10.4236/apm.2023.139041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.\",\"PeriodicalId\":43512,\"journal\":{\"name\":\"Advances in Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4236/apm.2023.139041\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4236/apm.2023.139041","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
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