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Regular and Chaotic Dynamics, 2025, Volume 30, Issue 4, Pages 464–480
DOI: https://doi.org/10.1134/S1560354725040021 (Mi rcd1316) 		 
Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

Spinning Top in Quadratic Potential and Matrix Dressing Chain

Vsevolod E. Adlera, Alexander P. Veselovb

a Landau Institute for Theoretical Physics, pr. Semenova 1A, 142432 Chernogolovka, Russia
b Department of Mathematical Sciences, Loughborough University, LE11 3TU Loughborough, UK
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DOI: https://doi.org/10.1134/S1560354725040021
Abstract: We show that the equations of motion of a rigid body about a fixed point in the Newtonian field with a quadratic potential are special reduction of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. Some new explicit solutions of the corresponding matrix system and the spectral properties of the related Schrödinger operators are discussed.
Keywords: rigid body dynamics, matrix Schrödinger operators, Darboux transformations
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: 24.04.2025
Accepted: 01.07.2025
Document Type: Article
MSC: 37J35, 70H06, 81R12
Language: English
Citation: Vsevolod E. Adler, Alexander P. Veselov, “Spinning Top in Quadratic Potential and Matrix Dressing Chain”, Regul. Chaotic Dyn., 30:4 (2025), 464–480
Citation in format AMSBIB
\Bibitem{AdlVes25}
\by Vsevolod E. Adler, Alexander P. Veselov
\paper Spinning Top in Quadratic Potential and Matrix Dressing Chain
\jour Regul. Chaotic Dyn.
\yr 2025
\vol 30
\issue 4
\pages 464--480
\mathnet{http://mi.mathnet.ru/rcd1316}
\crossref{https://doi.org/10.1134/S1560354725040021}
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