
This article is cited in 1 scientific paper (total in 1 paper)
Examples of topological approach to the problem of inverted pendulum with moving pivot point
Ivan Yu. Polekhin^{} ^{} Lomonosov Moscow State University, GSP1, Leninskie Gory 1, Moscow, 119991, Russia
Abstract:
Two examples concerning application of topology in study of dynamics of inverted plain mathematical pendulum with pivot point moving along horizontal straight line are considered. The first example is an application of the Ważewski principle to the problem of existence of solution without falling. The second example is a proof of existence of periodic solution in the same system when law of motion is periodic as well. Moreover, in the second case it is also shown that along obtained periodic solution pendulum never becomes horizontal (falls).
Keywords:
inverted pendulum, Lefschetz–Hopf theorem, Ważewski principle, periodic solution.
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UDC:
5172
MSC: 70K40, 70G40, 37B55 Received: 13.09.2014 Revised: 19.11.2014
Citation:
Ivan Yu. Polekhin, “Examples of topological approach to the problem of inverted pendulum with moving pivot point”, Nelin. Dinam., 10:4 (2014), 465–472
Citation in format AMSBIB
\Bibitem{Pol14}
\by Ivan~Yu.~Polekhin
\paper Examples of topological approach to the problem of inverted pendulum with moving pivot point
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 4
\pages 465472
\mathnet{http://mi.mathnet.ru/nd457}
\zmath{https://zbmath.org/?q=an:06430346}
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http://mi.mathnet.ru/eng/nd457 http://mi.mathnet.ru/eng/nd/v10/i4/p465
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This publication is cited in the following articles:

S. V. Bolotin, V. V. Kozlov, “Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problem”, Izv. Math., 79:5 (2015), 894–901

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