Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems
Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the...
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| Published in | International journal of non-linear mechanics Vol. 90; pp. 32 - 38 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Elsevier Ltd
01.04.2017
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0020-7462 1878-5638 |
| DOI | 10.1016/j.ijnonlinmec.2017.01.003 |
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| Abstract | Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results.
•Fractional generalized Birkhoff equations within Riemann-Liouville fractional derivatives are established.•Fractional Noether identity and fractional Noether theorem for the fractional generalized Birkhoffian system are presented.•Perturbation to the fractional generalized quasi-symmetry and the fractional adiabatic invariants are investigated.•The classical generalized Birkhoffian system and the fractional Birkhoffian system are discussed as special cases. |
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| AbstractList | Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results.
•Fractional generalized Birkhoff equations within Riemann-Liouville fractional derivatives are established.•Fractional Noether identity and fractional Noether theorem for the fractional generalized Birkhoffian system are presented.•Perturbation to the fractional generalized quasi-symmetry and the fractional adiabatic invariants are investigated.•The classical generalized Birkhoffian system and the fractional Birkhoffian system are discussed as special cases. Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results. |
| Author | Zhang, Yi Song, Chuan-Jing |
| Author_xml | – sequence: 1 givenname: Chuan-Jing surname: Song fullname: Song, Chuan-Jing email: songchuanjingsun@126.com organization: College of Science, Nanjing University of Science and Technology, Nanjing 210094, China – sequence: 2 givenname: Yi surname: Zhang fullname: Zhang, Yi email: weidiezh@gmail.com organization: College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China |
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| Keywords | Conserved quantity Riemann-Liouville fractional derivative Adiabatic invariant Generalized Birkhoffian system |
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| SubjectTerms | Adiabatic flow Adiabatic invariant Conserved quantity Deformation Derivatives Generalized Birkhoffian system Invariants Mechanics Riemann-Liouville fractional derivative Symmetry |
| Title | Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems |
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