Borisov, A. V.; Ryabov, P. E.; Sokolov, S. V. 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. Cited in 2 Documents 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 Keywords:completely integrable Hamiltonian systems; Lagrange top; focus singularities PDFBibTeX XMLCite \textit{A. V. Borisov} et al., Dokl. Math. 102, No. 3, 468--471 (2020; Zbl 1482.37054); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 26--30 (2020) Full Text: DOI References: [1] A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems: Geometry, Topology, Classification (Udmurt. Univ., Izhevsk, 1999; Chapman and Hall/CRC, Boca Raton, 2004). · Zbl 1053.37518 [2] Ryabov, P. E.; Oshemkov, A. A.; Sokolov, S. V., Regul. Chaotic Dyn., 21, 581-592 (2016) · Zbl 1368.70029 · doi:10.1134/S1560354716050087 [3] Markeev, A. P., Dokl. Phys., 54, 392-396 (2009) · Zbl 1342.70017 · doi:10.1134/S1028335809080114 [4] Markeev, A. P., J. Appl. Math. Mech., 75, 132-139 (2011) · Zbl 1272.70055 · doi:10.1016/j.jappmathmech.2011.05.002 [5] Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S., Russ. Math. Surv., 65, 259-318 (2010) · Zbl 1202.37077 · doi:10.1070/RM2010v065n02ABEH004672 [6] Markeev, A. P., Mech. Solids, 47, 373-379 (2012) · doi:10.3103/S0025654412040012 [7] Ngoc, San Vu, Topology, 42, 365-380 (2003) · Zbl 1012.37041 · doi:10.1016/S0040-9383(01)00026-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.