Effective Computations in Celestial Mechanics and Astrodynamics

(CISM Course on ``Modern Methods of Analytical Mechanics
and their Applications'', Udine, June 16 to 20, 1997)

Carles Sim\'o, Departament de Matem\`atica Aplicada i An\`alisi,
   Universitat de Barcelona  Gran Via 585, 08007 Barcelona

Problems in Celestial Mechanics and Astrodynamics are considered under
the point of view of Hamiltonian Dynamical Systems. A main tool to
analyze the dynamics consists in studying the {\em skeleton} of the
system, that is, the invariant objects (fixed points, periodic orbits
and invariant tori) as well as their related stable, unstable and centre
manifolds. Methods to compute these objects are presented. They are
analytical, with the symbolic implementacion, purely numerical or a
combination of both. Several examples are presented.
