This article is cited in 3 scientific papers (total in 3 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
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).
inverted pendulum, Lefschetz–Hopf theorem, Ważewski principle, periodic solution.
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MSC: 70K40, 70G40, 37B55
Ivan Yu. Polekhin, “Examples of topological approach to the problem of inverted pendulum with moving pivot point”, Nelin. Dinam., 10:4 (2014), 465–472
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\paper Examples of topological approach to the problem of inverted pendulum with moving pivot point
\jour Nelin. Dinam.
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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
I. Polekhin, “On motions without falling of an inverted pendulum with dry friction”, J. Geom. Mech., 10:4 (2018), 411–417
I. Polekhin, “On topological obstructions to global stabilization of an inverted pendulum”, Syst. Control Lett., 113 (2018), 31–35
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