A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics

Abstract

The main aim of this paper is to build up a set of semi-analytical integrators based on the use of a class of anomalies defined by means of a generalized Sundman transformation. The integrators are based on the developments of the mean anomaly and the vector radius according to the new anomaly. To manipulate these developments, a Poisson series processor called poison.h has been used. This processor has been written as a C++class and it contains a set of methods to manage the most common arithmetic and functional operations with these objects.

Keywords:

• celestial mechanics
• planetary theories
• algorithms
• orbital mechanics
• perturbation theory
• computational algebra

2010 AMS Subject Classifications :

• 70F05
• 70F10
• 70F15
• 70M20

Acknowledgements

This research has been partially supported by Grant GV/2009/027 from the Generalitat Valenciana and Grant P1-06I455.01/1 from Bancaja.