Noether's theorems for nonshifted dynamic systems on time scales

摘要

Conserved quantities on time scales for the nonshifted Birkhoffian system and the nonshifted Hamiltonian system are investigated. Firstly, nonshifted Birkhoff equation and nonshifted Hamilton equation on time scales are obtained. Secondly, Noether identities and Noether theorems for the nonshifted Birkhoffian system and the nonshifted Hamiltonian system are achieved. Thirdly, special cases such as the classical Birkhoffian system, the discrete Birkhoffian system, the classical Hamiltonian system, the discrete Hamiltonian system and the nonshifted Lagrangian system are discussed.