Non-canonical perturbations in symplectic integration

The inclusion of non-canonical perturbations in symplectic integration schemes has been discussed. A rigorous derivation of an analog for theWisdom–Holman (1991) method, such that velocity dependent forces can be included, has been outlined. This is done both by using the δfunction formalism and also by means of formal Hamiltonization. Application to the relativistic corrections in Solar System integrations is discussed as an example. Numerical experiments confirm the usefulness of the method. This revised version was published online in July 2006 with corrections to the Cover Date.