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On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point. (English. Russian original) Zbl 1482.37054

Dokl. Math. 102, No. 3, 468-471 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 26-30 (2020).
Summary: We consider a completely integrable Hamiltonian system with two degrees of freedom that describes the dynamics of a Lagrange top with a vibrating suspension point. The results of a stability analysis of equilibrium positions are clearly presented. It turns out that, in the case of a vibrating suspension point, both equilibrium positions can be unstable, which corresponds to the existence of focus singularities in the considered model.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
70E40 Integrable cases of motion in rigid body dynamics
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics
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