85-85
1988-01-01
en
false
A Perturbative Method for Problems with Two Critical Arguments
chapter
https://scigraph.springernature.com/explorer/license/
chapters
Resonance in the restricted three body problem usually lead by averaging to one-degree of freedom Hamiltonian systems described by the Hamiltonian Ho (p,P). Consideration of a further degree of freedom, such as a fourth body or the ellipticity of the orbit of the perturbing body, may introduce a second critical argument (q) in the averaged system which will then be described by the Hamiltonian H = Ho (p,P) + ε H1 (p,q,P,Q). In a recent paper (Henrard-Lemaître, 1986) we have developed a semi-numerical perturbation method to deal with such systems even when the “unperturbed” Hamiltonian HO possesses critical curves in the region of interest. This method is based upon the fact that the solution of the Hamilton-Jacobi equation by which one usually introduce the action-angle variables do have a geometrical interpretation. The action variable is an area and the angular variable is a normalized time along the orbit. These quantities can be computed numerically even for fairly complex “unperturbed” systems. This method is used by A. Lemaître to unravel the complexity of the motion of asteroids in the Jovian resonance 2/1 taking into account the eccentricity of Jupiter.
http://link.springer.com/10.1007/978-94-009-2917-3_13
1988
2019-04-15T13:25
Information and Computing Sciences
pub.1004497946
dimensions_id
doi
10.1007/978-94-009-2917-3_13
Springer Netherlands
Dordrecht
Jacques
Henrard
University of Namur
Department of Mathematics, F.N.D.P., Rempart de la Vierge, 8, B-5000 Namur, Belgium
978-94-010-7813-9
The Few Body Problem
978-94-009-2917-3
Artificial Intelligence and Image Processing
Springer Nature - SN SciGraph project
M. J.
Valtonen
156ea3513f40622ec8e5e0c15b8610fad0f320d5ff50b3af14a343445595cf2a
readcube_id