Mei Symmetry for Constrained Mechanical System on Time Scales

Mei symmetry on time scales is investigated for Lagrangian system,Hamiltonian system,and Birkhoffian system.The main results are divided into three sections.In each section,the definition and the criterion of Mei symmetry are first presented.Then the conserved quantity deduced from Mei symmetry is obtained,and perturbation to Mei symmetry and adiabatic invariant are studied.Finally,an example is given to illustrate the methods and results in each section.The conserve quantity achieved here is a special case of adiabatic invariant.And the results obtained in this paper are more general because of the definition and property of time scale.

变阶分数阶广义Birkhoff系统的绝热不变量

基于Caputo变阶分数阶导数研究广义Birkhoff系统对称性的摄动与绝热不变量。作为特例,同时也讨论了变阶分数阶Birkhoff系统、分数阶广义Birkhoff系统及整数阶广义Birkhoff系统的绝热不变量。最后,举例说明结果的应用。