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Regular and Chaotic Dynamics, 2022, Volume 27, Issue 4, Pages 443–459
DOI: https://doi.org/10.1134/S1560354722040049
(Mi rcd1174)
 

This article is cited in 1 scientific paper (total in 1 paper)

Alexey Borisov Memorial Volume

The Harmonic Lagrange Top and the Confluent Heun Equation

Sean R. Dawson, Holger R. Dullin, Diana M.H. Nguyen

School of Mathematics and Statistics, University of Sydney, 2006 New South Wales, Australia
Citations (1)
References:
Abstract: The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson structure on $T^*S^3$. This global description naturally leads to a rational parametrisation of the set of critical values of the energy-momentum map. We show that there are 4 different topological types for generic parameter values. The quantum mechanics of the harmonic Lagrange top is described by the most general confluent Heun equation (also known as the generalised spheroidal wave equation). We derive formulas for an infinite pentadiagonal symmetric matrix representing the Hamiltonian from which the spectrum is computed.
Keywords: symmetric rigid body, Lagrange top, Hamiltonian Hopf bifurcation, quantisation, confluent Heun equation.
Received: 01.11.2021
Accepted: 13.06.2022
Bibliographic databases:
Document Type: Article
MSC: 70E17, 81Q99
Language: English
Citation: Sean R. Dawson, Holger R. Dullin, Diana M.H. Nguyen, “The Harmonic Lagrange Top and the Confluent Heun Equation”, Regul. Chaotic Dyn., 27:4 (2022), 443–459
Citation in format AMSBIB
\Bibitem{DawDulNgu22}
\by Sean R. Dawson, Holger R. Dullin, Diana M.H. Nguyen
\paper The Harmonic Lagrange Top
and the Confluent Heun Equation
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 4
\pages 443--459
\mathnet{http://mi.mathnet.ru/rcd1174}
\crossref{https://doi.org/10.1134/S1560354722040049}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4462432}
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  • https://www.mathnet.ru/eng/rcd/v27/i4/p443
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:89
    References:29
     
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