  We discuss an extension of the velocity Verlet method that accurately
approximates the kinetic-energy-conserving charged particle motion that comes
from magnetic forcing. For a uniform magnetic field, the method is shown to
conserve both particle kinetic energy and magnetic dipole moment better than
midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to
generate trapped particle trajectories, both in a cylindrical magnetic mirror
machine setup, and for dipolar fields like the earth's magnetic field. Finally,
the method is used to compute an example of (single) mirror motion in the
presence of a magnetic monopole field, where the trajectory can be described in
closed form.
