Abstract
This paper focuses on studying Noether’s theorems for dynamical systems with two kinds of non-standard Hamiltonians, respectively, namely exponential Hamiltonian and power-law Hamiltonian. Firstly, the differential equations of motion for dynamical systems with exponential Hamiltonian and power-law Hamiltonian are established. Secondly, according to the invariance of the action under the infinitesimal transformations, the definitions and criteria of Noether symmetric transformations and Noether quasi-symmetric transformations are given. Then, Noether’s theorems for dynamical systems with exponential Hamiltonian and power-law Hamiltonian are obtained, respectively. Finally, two examples are given to illustrate the applications of the results.
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Song, J., Zhang, Y. Noether’s theorems for dynamical systems of two kinds of non-standard Hamiltonians. Acta Mech 229, 285–297 (2018). https://doi.org/10.1007/s00707-017-1967-4
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DOI: https://doi.org/10.1007/s00707-017-1967-4