Does anybody knows where I can find a celestial mechanics library for maple?
To my knowledge, no such library exists, and indeed there is even not much literature on using Maple in celestial mechanics (although I think J. Laskar did use it for this purpose).
I do know that Maple does handle Poisson series; there is something in the on-line help about this.
You might also like to consult V.A. Brumberg’s "Analytical Techniques of Celestial Mechanics", which is a detailed discussion of the use of computer algebra in celestial mechanics (there are also lots of references).
Several years ago, Carl Murray and I used Maple and Mathematica to carry out an expansion of the planetary disturbing function, the multivariate Poisson series which is the starting point of much of celestial mechanics.
This work was described in the December 1994 special issue of the Maple Technical Newsletter (pages 24-28).
In the Maple version, we found that ’convert/trig’ was very inefficient at handling the very large Poisson series, so we changed all trigonometric quantities into polynomials in terms of complex exponentials.
We still had to break the calculation down into smaller chunks in order to avoid exceeding the limit (at that time) of 32k terms in a single expression.
I join David Holmgren in recommending Victor Brumberg’s "Analytical Techniques of Celestial Mechanics" as an excellent source book for the application of computer algebra to celestial mechanics.
Victor describes the algorithms in a way that isn’t dependent on a specific computer algebra system.