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2013
Impact Factor

# Sean Dawson

## Publications:

 Dawson S. R., Dullin H. R., Nguyen D. M. The Harmonic Lagrange Top and the Confluent Heun Equation 2022, vol. 27, no. 4, pp.  443-459 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 Citation: Dawson S. R., Dullin H. R., Nguyen D. M.,  The Harmonic Lagrange Top and the Confluent Heun Equation, Regular and Chaotic Dynamics, 2022, vol. 27, no. 4, pp. 443-459 DOI:10.1134/S1560354722040049