Symplectic mappings in asteroidal dynamics

Author(s)

Fernando Virgilio Roig

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto Astronômico e Geofísico (IAG/SBD)
• Defense date: 1997-08-08

Examining board members

Sylvio Ferraz de Mello; Ricardo Reis Cordeiro; Tatiana Alexandrovna Michtchenko

• Advisor: Sylvio Ferraz de Mello

Abstract

In this work, we developed a symplectic mapping which allow us to study the dynamical behaviour of asteroidal resonances in the frame of the non-planar elliptic restricted three-body problem. To obtain such a mapping we combine a symplectic scheme similar to that of Hadjidemetriou (1986) together with an asymmetric expansion of the disturbing funtion (Ferraz-Mello, 1987) which takes into account the inclinations of both the perturber and the disturbed bodies (Roig et al., 1997). This mapping is applied to the 2/1 and 3/2 mean motion resonances in the asteroidal belt. We explore a wide range of initial conditions in the phase space in order to get a large number of results which allow us to make some statistical conclusions about the generation of diffusion mechanisms acting in these resonances. (AU)