{"title":"分数阶拉格朗日系统与分数阶Birkhoffian系统的摄动理论","authors":"Song Chuanjing, Z. Yi","doi":"10.16356/J.1005-1120.2018.02.353","DOIUrl":null,"url":null,"abstract":"Perturbation to symmetry and adiabatic invariants are studied for the fractional Lagrangian system and the fractional Birkhoffian system in the sense of Riemann-Liouville derivatives. Firstly, the fractional Euler-Lagrange equation, the fractional Birkhoff equations as well as the fractional conservation laws for the two systems are listed. Secondly, the definition of adiabatic invariant for fractional mechanical system is given, then perturbation to symmetry and adiabatic invariants are established for the fractional Lagrangian system and the fractional Birkhoffian system under the special and general infinitesimal transformations, respectively. Finally, two examples are devoted to illustrate the results.","PeriodicalId":39730,"journal":{"name":"Transactions of Nanjing University of Aeronautics and Astronautics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perturbation Theory of Fractional Lagrangian System and Fractional Birkhoffian System\",\"authors\":\"Song Chuanjing, Z. Yi\",\"doi\":\"10.16356/J.1005-1120.2018.02.353\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Perturbation to symmetry and adiabatic invariants are studied for the fractional Lagrangian system and the fractional Birkhoffian system in the sense of Riemann-Liouville derivatives. Firstly, the fractional Euler-Lagrange equation, the fractional Birkhoff equations as well as the fractional conservation laws for the two systems are listed. Secondly, the definition of adiabatic invariant for fractional mechanical system is given, then perturbation to symmetry and adiabatic invariants are established for the fractional Lagrangian system and the fractional Birkhoffian system under the special and general infinitesimal transformations, respectively. Finally, two examples are devoted to illustrate the results.\",\"PeriodicalId\":39730,\"journal\":{\"name\":\"Transactions of Nanjing University of Aeronautics and Astronautics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of Nanjing University of Aeronautics and Astronautics\",\"FirstCategoryId\":\"1087\",\"ListUrlMain\":\"https://doi.org/10.16356/J.1005-1120.2018.02.353\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of Nanjing University of Aeronautics and Astronautics","FirstCategoryId":"1087","ListUrlMain":"https://doi.org/10.16356/J.1005-1120.2018.02.353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Engineering","Score":null,"Total":0}
Perturbation Theory of Fractional Lagrangian System and Fractional Birkhoffian System
Perturbation to symmetry and adiabatic invariants are studied for the fractional Lagrangian system and the fractional Birkhoffian system in the sense of Riemann-Liouville derivatives. Firstly, the fractional Euler-Lagrange equation, the fractional Birkhoff equations as well as the fractional conservation laws for the two systems are listed. Secondly, the definition of adiabatic invariant for fractional mechanical system is given, then perturbation to symmetry and adiabatic invariants are established for the fractional Lagrangian system and the fractional Birkhoffian system under the special and general infinitesimal transformations, respectively. Finally, two examples are devoted to illustrate the results.