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Examples of topological approach to the problem of inverted pendulum with moving pivot point. (Russian. English summary) Zbl 1353.70051
Summary: 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).

MSC:
70K40 Forced motions for nonlinear problems in mechanics
70G40 Topological and differential topological methods for problems in mechanics
37B55 Topological dynamics of nonautonomous systems
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