2021
DOI: 10.1016/j.jde.2021.02.062
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Parametric stability of a charged pendulum with oscillating suspension point

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Cited by 10 publications
(8 citation statements)
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“…In the articles [1,2,[5][6][7] we have used the expression parametric stability in the sense that the Hamiltonian depends on parameters, and studied the regions in the parameter space corresponding to the unstable systems of the parametric family (regions of parametric resonance) and the regions that correspond to the stable systems of the parametric family of Hamiltonians. In these articles we have not made a formal definition of parametric stability.…”
Section: Stability Of Periodic Linear Hamiltonian Systemsmentioning
confidence: 99%
“…In the articles [1,2,[5][6][7] we have used the expression parametric stability in the sense that the Hamiltonian depends on parameters, and studied the regions in the parameter space corresponding to the unstable systems of the parametric family (regions of parametric resonance) and the regions that correspond to the stable systems of the parametric family of Hamiltonians. In these articles we have not made a formal definition of parametric stability.…”
Section: Stability Of Periodic Linear Hamiltonian Systemsmentioning
confidence: 99%
“…A strongly localized forcing of a pendulum without dissipation is also obtained by an electrostatic rather than magnetic interaction, e.g., when the bob and an external body are electrically charged. Such cases were recently studied for idealized setups [17,18].…”
Section: Introductionmentioning
confidence: 99%
“…Minimum values of B for instability as functions of C from the harmonic balancing method for (a) subharmonic and (b) harmonic cases. The approximate power laws(18) and (19) are shown as thin solid and dashed straight lines…”
mentioning
confidence: 99%
“…Kapitza [3], [4]. Let us also mention some recent papers on the considering problem [5]- [8]. The comprehensive bibliography can hardly be listed here.…”
Section: Introductionmentioning
confidence: 99%