Nonintegrability of the problem of a spherical top rolling on a vibrating plane

DOI10.35634/vm200407zbMath1479.70017OpenAlexW3115531046MaRDI QIDQ4986779

Elena N. Pivovarova, Alexander A. Kilin

Publication date: 28 April 2021

Published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vuu746

zbMATH Keywords

chaosnonintegrabilityseparatrix splittingspherical topMelnikov's integralLagrange caseperiod advance mapvibrating plane

Mathematics Subject Classification ID

Dynamical systems in solid mechanics (37N15) Motion of a rigid body in contact with a solid surface (70E18) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (5)

A top on a vibrating base: new integrable problem of nonholonomic mechanics ⋮ Stabilization of steady rotations of a spherical robot on a vibrating base using feedback ⋮ The influence of the first integrals and the rolling resistance model on tippe top inversion ⋮ A particular integrable case in the nonautonomous problem of a Chaplygin sphere rolling on a vibrating plane ⋮ Motion control of the spherical robot rolling on a vibrating plane

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