Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-05-28
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Based on El-Nabulsi dynamical model for a non-conservative system, the problem of perturbation to Noether symmetries and adiabatic invariants of a Birkhoffian system under the action of a small disturbance is proposed and studied.
Firstly, the El-Nabulsi-Pfaff variational problem from extended exponentially fractional integral is presented and the El-Nabulsi-Birkhoff equations are established.
Secondly, the definitions and the criterions criteria of the Noether symmetric transformations and quasisymmetric transformations of the Birkhoffian system are given, and the Noether theorems of the system are established, which reveal the inner relationship between the Noether symmetries and the conserved quantities.
Thirdly, the perturbation of Noether symmetries under a small disturbance is studied, and corresponding adiabatic invariants are obtained.
As special cases, the deductions in nonconservative Hamiltonian system and nonconservative Lagrangian system and standard Birkhoffian system are given.
At the end of the paper, the case known as Hojman-Urrutia problem is discussed to investigate the Noether symmetries and the adiabatic invariants, the perturbation to Noether symmetries and the adiabatic invariants under El-Nabulsi dynamical model.
American Psychological Association (APA)
Zhang, Yi. 2015. Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074704
Modern Language Association (MLA)
Zhang, Yi. Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems. Mathematical Problems in Engineering No. 2015 (2015), pp.1-10.
https://search.emarefa.net/detail/BIM-1074704
American Medical Association (AMA)
Zhang, Yi. Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074704
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074704