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Neumann system, spherical pendulum and magnetic fields

Pavle Saksida

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In this paper we study a certain magnetic-like perturbation of the Neumann system. We prove the integrability of this system and show how its solutions are related to the solutions of a charged spherical pendulum influenced by the topologically nontrivial magnetic field Bd(q) = q/midqmid3 of the Dirac monopole. In the case when the quadratic potential of the Neumann system has a suitable axial symmetry, our system describes the motion of a charged particle under the influence of the potential and the homogeneous magnetic field Bh(q) = (1, 0, 0).


PACS

02.30.Ik Integrable systems

MSC

83C50 Electromagnetic fields

70H06 Completely integrable systems and methods of integration

Subjects

Mathematical physics

Dates

Issue 25 (28 June 2002)

Received 4 December 2001, in final form 26 March 2002

Published 14 June 2002



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