Abstract
Using purely elementary methods, necessary and sufficient conditions are given for the existence of 2T-periodic and 4T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating with period 2T. The equation of the motion is of the form
where l, g are constants and
A, T are positive constants. The exact stability zones for the upper equilibrium are presented.
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Supported by the Hungarian National Foundation for Scientific Research (OTKA) K109782.
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Csizmadia, L., Hatvani, L. On the existence of periodic motions of the excited inverted pendulum by elementary methods. Acta Math. Hungar. 155, 298–312 (2018). https://doi.org/10.1007/s10474-018-0835-6
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DOI: https://doi.org/10.1007/s10474-018-0835-6