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Periodic Solutions for the Eccentricity and Inclination First Order Resonance

Published online by Cambridge University Press:  07 August 2017

Marisa A. Nitto  and
Wagner Sessin
Marisa A. Nitto
Affiliation:
Depto. de Mecânica do Vôo e Orbital Instituto Tecnológico de Aeronáutica 12225, São José dos Campos, SP, Brasil
Wagner Sessin
Affiliation:
Depto. de Mecânica do Vôo e Orbital Instituto Tecnológico de Aeronáutica 12225, São José dos Campos, SP, Brasil

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For the first order resonance, the problem of the motion of two small masses around a primary body can be of three different types: eccentricity, inclination or eccentricity-inclination. The eccentricity type resonance problem has been the subject of several works since Poincaré(1902). The inclination type resonance problem was studied by Greenberg(1973) who used a particular reference system to obtain an integrable auxiliary system. Sessin and Ferraz-Mello(1984) studied the eccentricity type resonance problem considering the eccentricities of the orbits of the two small masses. Sessin(1991) study the inclination type resonance problem for an arbitrary reference system. In this paper we will study a dynamical system that includes both types of resonance. This study is based in the models developed by Sessin and Ferraz-Mello(1984) and Sessin(1991). The resulting system of differential equation is non-integrable; thus, the families of trivial periodic solutions are studied.

Type
Part IV - Planetary Satellites
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 231 - 232
Copyright
Copyright © Kluwer 1992 

References

Greenberg, R.:1973, Mon. Not.R. astr. Soc. 165, 305.CrossRefGoogle Scholar
Poincaré, H.:1902, Bull. Astron. 19, 290.Google Scholar
Sessin, W.: 1991, in these Proceedings.Google Scholar
Sessin, W. and Ferraz-Mello, S.:1984, Celest. Mech. 32, 307.CrossRefGoogle Scholar