  In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic
integrator was proposed for the integrable Kerr spacetime geometry. It is still
suited for simulating the nonintegrable dynamics of charged particles moving
around the Kerr black hole embedded in an external magnetic field. Its
successful construction is due to the contribution of a time transformation.
The algorithm exhibits a good long-term numerical performance in stable
Hamiltonian errors and computational efficiency. As its application, the
dynamics of order and chaos of charged particles is surveyed. In some
circumstances, an increase of the dragging effects of the spacetime seems to
weaken the extent of chaos from the global phase-space structure on Poincare
sections. However, an increase of the magnetic parameter strengthens the
chaotic properties. On the other hand, fast Lyapunov indicators show that there
is no universal rule for the dependence of the transition between different
dynamical regimes on the black hole spin. The dragging effects of the spacetime
do not always weaken the extent of chaos from a local point of view.
