Integrable systems of the ellipsoidal, paraboloidal and conical type with magnetic field

Author:

Fazlul Hoque MdORCID,Marchesiello AntonellaORCID,Šnobl LiborORCID

Abstract

Abstract We construct integrable Hamiltonian systems with magnetic fields of the ellipsoidal, paraboloidal and conical type, i.e. systems that generalize natural Hamiltonians separating in the respective coordinate systems to include nonvanishing magnetic field. In the ellipsoidal and paraboloidal case each this classification results in three one–parameter families of systems, each involving one arbitrary function of a single variable and a parameter specifying the strength of the magnetic field of the given fully determined form. In the conical case the results are more involved, there are two one–parameter families like in the other cases and one class which is less restrictive and so far resists full classification.

Funder

Ministry of Education, Youth and Sports of the Czech Republic

Gruppo Nazionale per la Fisica Matematica

Publisher

IOP Publishing

Reference30 articles.

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