Adiabatic Invariants for Generalized Fractional Birkhoffian Mechanics and Their Applications

摘要

Perturbation to Noether symmetry and adiabatic invariants are investigated for the generalized fractional Birkhoffian system with the combined Riemann-Liouville fractional derivative and the combined Caputo fractional derivative, respectively. Firstly, differential equations of motion for the generalized fractional Birkhoffian system are established. Secondly, Noether symmetry and conserved quantity are studied. Thirdly, perturbation to Noether symmetry and adiabatic invariants are presented for the generalized fractional Birkhoffian mechanics. And finally, several applications are discussed to illustrate the results and methods.