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Stability of an equilibrium position of a pendulum with step parameters
Institution:1. Dorodnicyn Computing Center of the Russian Academy of Sciences & Higher School of Economics, Russian Federation;2. Moscow State Technical University of Radio Engineering, Electronics, and Automation, Russian Federation;1. Candida Oancea Institute, Polytechnic University of Bucharest, Spl. Independentei 313, Bucharest 060042, Romania;2. Academia Romana, Calea Victoriei 125, Bucharest, Romania;1. Lunar and Planetary Laboratory, The University of Arizona, Tucson, AZ 85721-0092, USA;2. Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095-1567, USA;3. Department of Mathematical Sciences, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK
Abstract:A mathematical pendulum affected by parametric disturbance with potential energy being periodic step function is considered. Non-linear equation of the pendulum depends on two parameters characterizing the mean value in time of the parametric disturbance and range of its “ripple”. Values of the parameters can be set arbitrarily. The non-linear problem of stability for two particular solutions of the equation corresponding to a hanging and inverse pendulum is solved.
Keywords:Parametric oscillations  Stability  Resonance  Map
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