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Adiabatic invariants for disturbed fractional Hamiltonian system in terms of Herglotz differential variational principle
Acta Mechanica ( IF 2.7 ) Pub Date : 2020-09-08 , DOI: 10.1007/s00707-020-02796-3
Xin-Xin Xu , Yi Zhang

Based on the differential variational principle of Herglotz type, we reveal the internal relation between the perturbation and the adiabatic invariants for fractional Hamiltonian system with combined Caputo derivatives. First, based on the Herglotz variational problem, the Herglotz differential variational principle for fractional Hamiltonian systems is derived, and the fractional Hamilton canonical equations are given. Second, by introducing the infinitesimals, the transformation of the invariance condition of the Herglotz differential variational principle is established and an exact invariant of the system is derived. Third, the adiabatic invariants of Herglotz type for the disturbed fractional Hamiltonian system is obtained. Finally, the fractional linear damped oscillator of Herglotz type is discussed as an example to demonstrate the results.

中文翻译:

Herglotz微分变分原理中扰动分数哈密顿系统的绝热不变量

基于Herglotz型微分变分原理,我们揭示了带有组合Caputo导数的分数Hamilton系统的摄动与绝热不变量之间的内在关系。首先,基于Herglotz变分问题,推导了分数阶Hamilton系统的Herglotz微分变分原理,给出分数阶Hamilton正则方程。其次,通过引入无穷小,建立了Herglotz微分变分原理不变条件的变换,推导出系统的一个精确不变量。第三,获得了扰动分数哈密顿系统的Herglotz型绝热不变量。最后,以 Herglotz 型分数线性阻尼振荡器为例来说明结果。
更新日期:2020-09-08
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