Abstract
The new action of a nonstandard \(S=\int _a^b {e^{[p\dot{q}-H(p,q,t)]}dt}\) with a nonstandard Hamiltonian is introduced. The nonstandard Hamiltonian equations are obtained by using the standard variational method. Some new dynamical properties that the nonlinear systems hold are obtained. It is demonstrated that several constrained Hamiltonian systems have been identified to possess some interesting properties, and some additional features are discussed in details.
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Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grants Nos. 11472124, 11572145 and 11301350, and the Dr. Start-up fund in Liaoning Province of China under Grants No. 20141050, and the General science and technology Research Plans of Liaoning Educational Bureau of China under Grants No. L2013005, and China Postdoctoral Science Foundation Grants No. 2014M560203
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Liu, S., Guan, F., Wang, Y. et al. The nonlinear dynamics based on the nonstandard Hamiltonians. Nonlinear Dyn 88, 1229–1236 (2017). https://doi.org/10.1007/s11071-016-3306-z
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DOI: https://doi.org/10.1007/s11071-016-3306-z