New formulation of de Sitter's theory of motion for Jupiter I  IV. I. Equations of motion and the disturbing function.
Abstract
Elliptic orbits are substituted for circular orbits in the first approximation, in an analysis of the common retrograde motion of Jupiter's satellites. A modification of the de Sitter theory, made possible by extended observations of the satellites, is presented with attention to that aspect of the theory which eliminates small divisors at all stages of the solution. The convergence problem is circumvented by use of Poincare's canonical relative coordinates. In addition, modified Delaunay variables and their associated Poincare variables are applied to the disturbing function, which is expanded by means of generalized Newcomb operators.
 Publication:

IAU Colloq. 41: Dynamics of Planets and Satellites and Theories of their Motion
 Pub Date:
 1978
 DOI:
 10.1007/9789400998094_23
 Bibcode:
 1978ASSL...72..189A
 Keywords:

 Galilean Satellites;
 Jupiter (Planet);
 Orbit Calculation;
 Orbital Mechanics;
 Canonical Forms;
 Equations Of Motion;
 Poincare Problem;
 Astronomy;
 Galilean Satellites:Orbits