It is common in classical mechanics to encounter systems whose Hamiltonian H is the sum of an often exactly integrable Hamiltonian H _ { 0 } and a small perturbation \epsilon H _ { 1 } with \epsilon \ll 1 .
Such near-integrability can be exploited to construct particularly accurate operator splitting methods to solve the equations of motion of H .
However , in many cases , for example in problems related to planetary motion , it is computationally expensive to obtain the exact solution to H _ { 0 } .

In this paper we present a new family of embedded operator splitting ( EOS ) methods which do not use the exact solution to H _ { 0 } , but rather approximate it with yet another , embedded operator splitting method .
Our new methods have all the desirable properties of classical methods which solve H _ { 0 } directly .
But in addition they are very easy to implement and in some cases faster .
When applied to the problem of planetary motion , our EOS methods have error scalings identical to that of the often used Wisdom-Holman method but do not require a Kepler solver , nor any coordinate transformations , or the allocation of memory .
The only two problem specific functions that need to be implemented are the straight-forward kick and drift steps typically used in the standard second order leap-frog method .