ABSTRACT
It is a simple matter to convert second order problems into systems of first order equations amenable to conventional numerical integrators but, since they are relatively common, it is natural to seek new methods which can be applied directly with greater convenience. In particular, dynamical systems are based on forces which cause acceleration, the second order derivative of position. The gravitational two-body problem, used as a test case in earlier chapters, falls into this category. Special multistep formulae for second order problems also may be derived. These have become particularly popular in dynamical astronomy applications, although the use of Runge-Kutta-Nystrom formulae (RKN) methods has become more popular. Many second order systems do not contain explicitly any first derivative terms. As an example consider the restricted three-body gravitational problem and the cited program RKNG.
