Motion of a charge in a magnetic dipole field. I. Painlevé analysis and a conservative numerical scheme

摘要

We present a new numerical scheme to integrate the equations of motion of a charged particle in a magnetic dipole field. The scheme is time-inversion symmetry preserving, and it shows a discrete version of the two conserved quantities of the underlying continuous equation. We also present the Painlevé analysis of the system by using an approach which to our best knowledge is new.