Title:

                    Secular resonances in the asteroid belt - Theoretical perturbation approach and the problem of their
                    location
 Authors:

                    Morbidelli, Alessandro; Henrard, Jacques
 Affiliation:

                    AB(Facultes Universitaires Notre-Dame de la Paix, Namur, Belgium)
 Journal:

                    Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 51, no. 2, 1991, p. 131-167.
                    Research supported by CEC. (CeMDA Homepage)
 Publication Date:

                    00/1991
 Category:

                    Astrophysics
 Origin:

                    STI
 NASA/STI Keywords:

                    ASTEROID BELTS, ORBITAL MECHANICS, ORBITAL RESONANCES (CELESTIAL
                    MECHANICS), PERTURBATION THEORY, APPROXIMATION, COMPUTATIONAL
                    ASTROPHYSICS, HAMILTONIAN FUNCTIONS, PERIHELIONS
 Bibliographic Code:

                    1991CeMDA..51..131M
 

                                            Abstract

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach
avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the
inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle
variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the
asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An
explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the
masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series
expansion is discussed in the paper.