Noether Symmetries And Conserved Quantities For Nonholonomic Mechanical Systems On Time Scales

In this paper,the Noether theorems for nonholonomic mechanical systems on time scales are studied.The Noether symmetries and conserved quantities for nonholonomic mechanical systems of non-Chetaev's type in configuration space and phase space,Nabla variational problem and controllable nonholonomic systems on time scales are given respectively.Firstly,the Hamilton principle in configuration space on time scales is proposed,and the differential equations of motion for nonholonomic mechanical systems of non-Chetaev's type in configuration space on time scales are established.According to the invariance of the Hamilton action in configuration space on time scales under a group of infinitesimal transformations and using the method of time-re-parameterization,the Noether identity of nonholonomic mechanical systems of non-Chetaev's type in configuration space on time scales is given,and the corresponding conserved quantity is obtained.Secondly,the generalized momentum on time scales is proprosed,and the differential equations of motion for nonholonomic mechanical systems of non-Chetaev's type in phase space on time scales are established based on the Hamilton principle in phase space on time scales.According to the invariance of the Hamilton action in phase space on time scales under a group of infinitesimal transformations and using the method of time-re-parameterization,the Noether identity of nonholonomic mechanical systems of non-Chetaev's type in phase space on time scales is given,and the corresponding conserved quantity is obtained.Then,based on the relationship between the Delta calculus and the Nabla calculus on time scales and the theory of time scale,the nonholonomic Lagrange equation for Nabla variational problem on time scales is established.According to the invariance of the Hamilton action for Nabla variational problem on time scales under a group of infinitesimal transformations,the Noether identity of nonholonomic mechanical systems of Nabla variational problem on time scales is given,and the corresponding conserved quantity is obtained.Finally,proposed to add controllable parameters in the constraints,and the differential equations of motion for controllable nonholonomic mechanical systems on time scales are established based on the Hamilton principle on time scales.According to the invariance of the Hamilton action on time scales under a group of infinitesimal transformations and using the method of time-re-parameterization,the Noether identity of controllable nonholonomic mechanical systems on time scales is given,and the corresponding conserved quantity is obtained.