The symplectic character of the three-dimensional magnetic-binary problem (Q2266593)

The motion of a charged particle in the magnetic field generated by two massive spherical bodies is studied. The dipolar magnetic fields of these bodies are oriented along some constant axes and the gravitational effects are neglected. For the three dimensional case, the differential barycentric equations of motion as well as the equations for the first order variations are obtained. The symplectic matrix of the differential system is given. In order to check the accuracy of numerical computations, some relations between the variations are derived. This paper is a generalization of the corresponding planar motion [the first two authors, Acta Mech. 42, 135-141 (1982; Zbl 0481.70007)].