  We present a simple choice of integration variables that can be used to
exploit the near-integrable character of problems in celestial mechanics. The
approach is based on the well-known principle of variation of parameters:
instead of orbital elements, we use the phase-space coordinates the object
would have at a given point in its (Keplerian) orbit if the perturbing forces
were removed. This formulation is suitable for almost any numerical integrator;
thus, multistep schemes are easy to build, stepsize can be adjusted, and
dissipative forces are allowed. Compared with traditional non-symplectic N-body
integrators, the approach often offers increase in speed or accuracy if
perturbations are small.
