Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelin. Dinam., 2014, Volume 10, Number 4, Pages 465–472 (Mi nd457)  

This article is cited in 8 scientific papers (total in 8 papers)

Examples of topological approach to the problem of inverted pendulum with moving pivot point

Ivan Yu. Polekhin

Lomonosov Moscow State University, GSP-1, 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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Bibliographic databases:
UDC: 51-72
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 465--472
\mathnet{http://mi.mathnet.ru/nd457}
\zmath{https://zbmath.org/?q=an:06430346}


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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. I. Polekhin, “On motions without falling of an inverted pendulum with dry friction”, J. Geom. Mech., 10:4 (2018), 411–417  crossref  mathscinet  zmath  isi  scopus
    3. I. Polekhin, “On topological obstructions to global stabilization of an inverted pendulum”, Syst. Control Lett., 113 (2018), 31–35  crossref  mathscinet  zmath  isi  scopus
    4. R. Srzednicki, “On periodic solutions in the Whitney's inverted pendulum problem”, Discret. Contin. Dyn. Syst.-Ser. S, 12:7 (2019), 2127–2141  crossref  mathscinet  zmath  isi  scopus
    5. I. Yu. Polekhin, “Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces”, Rus. J. Nonlin. Dyn., 16:2 (2020), 343–353  mathnet  crossref  mathscinet
    6. Ivan Yu. Polekhin, “The Method of Averaging for the Kapitza – Whitney Pendulum”, Regul. Chaotic Dyn., 25:4 (2020), 401–410  mathnet  crossref  mathscinet
    7. Ivan Yu. Polekhin, “Some Results on the Existence of Forced Oscillations in Mechanical Systems”, Proc. Steklov Inst. Math., 310 (2020), 250–261  mathnet  crossref  crossref  isi  elib
    8. N. A. Stepanov, M. A. Skvortsov, “Lyapunov exponent for Whitney's problem with random drive”, JETP Letters, 112:6 (2020), 376–382  mathnet  crossref  crossref  isi  elib
  • Нелинейная динамика
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