A Study on Time Scale Non-Shifted Hamiltonian Dynamics and Noether's Theorems

The time-scale non-shifted Hamiltonian dynamics are investigated,including both general holonomic systems and nonholonomic systems.The time-scale non-shifted Hamilton principle is presented and extended to nonconservative system,and the dynamic equations in Hamiltonian framework are deduced.The Noether symmetry,including its definition and criteria,for time-scale non-shifted Hamiltonian dynamics is put forward,and Noether's theorems for both holonomic and nonholonomic systems are presented and proved.The nonshifted Noether conservation laws are given.The validity of the theorems is verified by two examples.