Geodesic
Examples of topological approach to the problem of inverted pendulum with moving pivot point
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 465-472

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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, Ważewski principle, periodic solution.
Mots-clés : Lefschetz–Hopf theorem 
@article{ND_2014_10_4_a5,
     author = {Ivan Yu. Polekhin},
     title = {Examples of topological approach to the problem of inverted pendulum with moving pivot point},
     journal = {Russian journal of nonlinear dynamics},
     pages = {465--472},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/}
}
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Ivan Yu. Polekhin. Examples of topological approach to the problem of inverted pendulum with moving pivot point. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 465-472. http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/