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A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems

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Abstract

For a generalized Hamiltonian system with the action of small forces of perturbation, the Lie symmetries, symmetrical perturbation, and adiabatic invariants is presented. Based on the invariance of equations of motion for the system under general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations, and exact invariants of the system are given. Then the determining equations of Lie symmetrical perturbation and adiabatic invariants of the disturbed systems are obtained. Furthermore, in the special infinitesimal transformations, two deductions are given. At the end of the paper, one example is given to illustrate the application of the method and result.

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Authors and Affiliations

  1. Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, P.R. China

    Wenan Jiang & Shaokai Luo

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  1. Wenan Jiang
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  2. Shaokai Luo
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Correspondence to Shaokai Luo.

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This work is partly supported by National Natural Science Foundation of China (Grant No. 10372053).

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Jiang, W., Luo, S. A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems. Nonlinear Dyn 67, 475–482 (2012). https://doi.org/10.1007/s11071-011-9996-3

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