Neumann system, spherical pendulum and magnetic fields Pavle Saksida Department of Mathematics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia E-mail: Pavle.Saksida@fmf.uni-lj.si Abstract. 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 non-trivial magnetic field B d (q)= q/q 3 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 B h (q) = (1, 0, 0). PACS numbers: 03.20, 02.20Sv AMS classification scheme numbers: 37J15, 53D20, 70H06 Submitted to: J. Phys. A: Math. Gen.