Nonshifted Adiabatic Invariant on Time Scale

摘要

Three aspects which include differential equation of motion, Noether symmetry and conserved quantity, perturbation to Noether symmetry and adiabatic invariant are investigated for the nonshifted Birkhoffian system, nonshifted Hamiltonian system and nonshifted Lagrangian system, respectively. Then, some relationships among the three mechanic systems and some special cases of the main results are presented. Finally, an example is given to illustrate the application of the methods and results.