| In this paper,dynamic modeling and symmetry of time-scales variable mass systems are studied.The establishment of kinetic equations and Noether symmetries and the conserved quantities of the nonhonomic system with variable mass in phase space,variable mass controllable nonholonomic systems relative to non-inertial systems,event space variable mass systems on time scales are studied.1.Based on the Hamilton principle corresponding to the nonholonomic system with variable mass in phase space on time scales,then the motion equations of variable mass nonholonomic system in the phase space and the corresponding holonomic system are derived on time scales,then the cirection of the Noether generalized quasi-symmetries of this system and corresponding holonomic system are given by the Noether equation and the limiting equation.Further,the corresponding conserved quantities of the systems are given.2.Based on the properties of time scales and Hamilton’s principle on time scales,the motion equation of the nonholonomic singular system with variable mass control on time scales is given,The Noether’s generalized quasi-symmetry of this system is defined and the corresponding conserved quantity is obtained.3.According to the related theories of calculus on time scales,the motion equation of variable mass system relative to the system with non-inertial on time scales is given.Then the generalized Noether equation of this system is given and the corresponding symmetry and conserved quantity are obtained.4.According to the motion equation of nonholonomic system with variable mass on time scales in Chater three and the related theory of event space,the equation of motion of the event space on time scales is further obtained.The generalized Noether equation of the invariance to Noether symmetry and the corresponding conserved quantities are given. |
