  In this paper we discuss epicycloid approximation of the trajectories of
charged particles in axisymmetric magnetic fields. Epicycloid trajectories are
natural in the Guiding Center approximation and we study in detail the errors
arising in this approach. We also discuss how using exact results for particle
motion in the equatorial plane of a magnetic dipole the accuracy of this
approximation can be significantly extended. We also show that the epicycloids
approximate the trajectory of a charged particle more accurately than the
position of the particle along the trajectory.
