{"paper":{"title":"Spherically restricted motion of a charge in the field of a magnetic dipole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"3), Canada (3) Member of SNI, D Cort\\'es-Poza (2) ((1) Departamento de F\\'isica, Emilio Cort\\'es (1, McGill University, M\\'exico), M\\'exico (2) Center for Intelligent Machines, Montreal, Universidad Aut\\'onoma Metropolitana Iztapalapa","submitted_at":"2013-01-11T06:19:45Z","abstract_excerpt":"We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\\\"oermer problem within a sphere, with the dipole in its centre. We start from a Lagrangian approach which allows us to analyze the dynamical properties of the system, such as the role of a velocity dependent potential, the symmetries and the conservation properties. We derive the Hamilton equations of motion and observe that in this restricted case the equations can be reduced to a quadrature. From the Hamiltonian function we find for the pola"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2393","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}