Astronomy and Astrophysics – Astrophysics
Scientific paper
2004-02-13
Astronomy and Astrophysics
Astrophysics
25 pages, 11 figures, to be published in "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Systems" (B.A.Steves,
Scientific paper
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes oscillates around a constant value. It introduces the Hamiltonian equations of the $N$-planet problem and Poincar\'e's reduction of them to $3N$ degrees of freedom with a detailed discussion of the non-osculating ``canonical'' heliocentric Keplerian elements that should be used with Poincar\'e relative canonical variables. It also includes Beaug\'e's approximation to expand the disturbing function in the exoplanetary case where masses and eccentricities are large. The paper is concluded with a discussion of systems captured into resonance and their evolution to symmetric and asymmetric stationary solutions with apsidal corotation.
Beauge Christian
Ferraz-Mello Sylvio
Michtchenko Tatiana A.
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