Using the paper "The orbits of the satellites of Mars determined from
Earth-based and spacecraft observations" by A.T. Sinclair (1989), show
how the values given in Table 5 of that paper are calculated.  The
values in that table are the rectangular equatorial positions
(relative to the center of Mars) of Phobos and Deimos for three dates.
 What I want is to see how the orbital elements given in Tables 2a and
2b of that paper are used to arrive at those values.  I expect details
such as formulas used as well as intermediate calculated values.

The paper can be found in PDF format at
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1989A%26A...220..321S&db_key=AST

In case you are wondering, no this isn't for schoolwork.  I've been
trying to solve this problem as a hobby project and am frustrated by
my own lack of knowledge and by the lack of examples of calculating
orbits which are based on intermediate (Laplace) planes.  I want an
explanation of the procedure for solving the orbit and, to assist in
debugging my code, I want intermediate calculated values.

Thanks!