Transactions of Nanjing University of Aeronautics & Astronautics
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Perturbation to Noether Symmetries and Adiabatic Invariants for Generalized Birkhoff Systems Based on El-Nabulsi Dynamical Model
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Abstract:
With the action of small perturbation on generalized El-Nabulsi-Birkhoff fractional equations, the perturbation to Noether symmetries and adiabatic invariants are studied under the framework of El-Nabulsi’s fractional model. Firstly, based on the invariance of El-Nabulsi-Pfaff action under the infinitesimal transformations of group, the exact invariants are given. Secondly, on the basis of the definition of higher order adiabatic invariants of a dynamical system, the adiabatic invariants of the Noether symmetric perturbation for disturbed generalized El-Nabulsi’s fractional Birkhoff system are presented under some conditions, and some special cases are discussed. Finally, an example known as Hojman-Urrutia problem is given to illustrate the application of the results.
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