  Symplectic integration algorithms have become popular in recent years in
long-term orbital integrations because these algorithms enforce certain
conservation laws that are intrinsic to Hamiltonian systems. For problems with
large variations in timescale, it is desirable to use a variable timestep.
However, naively varying the timestep destroys the desirable properties of
symplectic integrators. We discuss briefly the idea that choosing the timestep
in a time symmetric manner can improve the performance of variable timestep
integrators. Then we present a symplectic integrator which is based on
decomposing the force into components and applying the component forces with
different timesteps. This multiple timescale symplectic integrator has all the
desirable properties of the constant timestep symplectic integrators.
