XXXII Workshop on Geometric Methods in Physics | 30.06-6.07.2013 |

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## Ivailo Mladenov## Planar Motion of Charged Particles in a Magnetic Dipole FieldWe consider the system of Newton-Lorentz equations describing the planar non-relativistic motion of a charged particle of unit mass in a transverse magnetic dipole field. Actually, this system belongs to the class of dynamical systems of two degrees of freedom whose integrability in the Liouville-Arnold sense is studied in [1]. The magnitude of magnetic dipole field depends only on the distance from the origin and therefore (see [2]), the corresponding Newton-Lorentz system is integrable by quadratures since it possesses two functionally independent integrals of motion. In the present work, the techniques developed by the authors in [1, 2] are used to represent the trajectories of the particles in explicit analytic form in terms of Jacobian elliptic functions. [1] Vassilev V., Djondjorov P. and Mladenov I., Integrable Dynamical Systems of the Frenet–Seret Type. In: Proc. 9th International Workshop on Complex Structures, Integrability and Vector Fields, World Scientific, Singapore 2009, pp. 234-245. [2] Mladenov I., Hadzhilazova M., Djondjorov P. and Vassilev V., On the Plane Curves whose Curvature Depends on the Distance from the Origin, AIP Conf. Proc. vol. 1307, American Institute of Physics, New York 2010, pp. 112-118. |

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