2014/11/06 by Ivan Polekhin, Polekhin, Ivan
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS
paper · pdf · doi:10.48550/arxiv.1411.1585
arXiv admin note: substantial text overlap with arXiv:1407.4787, linguistic improvements
arxiv created 2015/08/10 · arxiv updated 2015/08/11
For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the pendulum never becomes horizontal along the considered periodic solution. Presented proof is an application of some recent results in the fixed point theory.