Mei Symmetry And Conserved Quantities Of A Mechanical System In Phase Space On Time Scales

In this paper,the theory of Mei symmetry for mechanical system on time scales are studies.What's more,the Mei symmetry for the Hamiltonian system?in phase space and of Appell equations for holonomic system on time scales are given,as the same time it also gives a method to calculate the Mei conserved quantity and Noether conserved quantity.According to the arbitrariness of time scales,this method can be extended to various mechanical system such as Birkhoff system and non-holonomic system.First of all,The Mei symmetry for Hamiltonian system on time scales is studied in this paper.The Hamilton principle on time scales is establishied.Based on the invariance of the Hamilton action on time scales under the infinitesimal transformations with respect to the time and generalized coordinates,the definition and criterion of Mei symmetry for Hamiltonian system are explored.Meanwhile the structural equation and conserved quantity of Mei system on time scales are obtained.Secondly,The Mei symmetry and the conserved quantity in phase space on time scales are studied in this paper.The dynamic differential equation in phase space on time scales is established which is rely on the Lagrange equations on time scales.Based on the invariance of the Hamilton action on time scales under the infinitesimal transformations with respect to the time and generalized coordinates,the definition and criterion of Mei symmetry in phase space on time scales are obtained.As the same time,the structure equation of Mei symmetry and the conserved quantity are obtained.Finally,The Mei symmetry and Mei conserved quantity of Appell equations for holonomic systems on time scales are studied in this paper.Under the infinitesimal transformations of groups,the definition and criterion of Mei symmetry of Appell equations for holonomic systems are given.Finally,Mei conserved quantity expressed by Appell functions are obtained.