Transactions of Nanjing University of Aeronautics & Astronautics
Non-Destructive Testing and Structural Health Monitoring in Aerospace 2018
Perturbation Theory of Fractional Lagrangian System and Fractional Birkhoffian System
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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.
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This work was supported by the National Natural Science Foundation of China (Nos.11272227,11572212) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province (No.KYLX15_0405).
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