resonance; asymmetric equilibria; stability; capture probability
Abstract :
[en] We study the position and the stability of the equilibria for a generic Hamiltonian function developed up to the second harmonic and depending on two parameters; we describe the topology of the phase space for fixed values of these parameters. We show that for some values of the parameters asymmetric equilibria (unstable or stable) may appear. We deduce the conditions of capture into first order resonances for slowly drifting systems. We apply this model to the restricted three-body problem.
Disciplines :
Mathematics
Author, co-author :
Jancart, Sylvie ; Facultés Universitaires Notre-Dame de la Paix - Namur - FUNDP > Mathématiques
Lemaitre, Anne; Département de mathématique FUNDP, 8, Rempart de la Vierge, B-5000 Namur, Belgique
Istace, Anne; Département de mathématique FUNDP, 8, Rempart de la Vierge, B-5000 Namur, Belgique)
Language :
English
Title :
Second Fundamental Model of Resonance with Asymmetric Equilibria
Borderies, N. and Goldreich, P.: 1984, 'A simple derivation of capture probabilities for the j + 1:j and j + 2:j orbit-orbit resonance problems', Celest. Mech. & Dyn. Astr. 32, 127-136.
Coffey, L. C., Deprit, A. and Deprit, E.: 1994, 'Frozen orbits for satellite close to an Earth-like planet', Celest. Mech. & Dyn. Astr. 59, 37-72.
Jancart, S. and Lemaitre, A.: 2001, 'Dissipative forces and external resonances', Celest. Mech. & Dyn. Astr. 81, 75-80.
Henrard, J.: 1982, 'Capture into resonance: an extension of the use of the adiabatic invariants', Celest. Mech. 27, 3-22.
Henrard, J.: 1993. 'The Adiabatic Invariant in Classical Mechanics', Dynamics Reported, Springer Verlag, 197-218.
Henrard, J. and Lemaitre, A.: 1983, 'Second fundamental model of resonance', Celest. Mech. 30, 117-235.
Lemaitre, A.: 1984, 'High-order resonances in the restricted three-body problem', Celest. Mech. & Dyn. Astr. 32, 109-126.
Malhotra, R.: 1990, 'Capture probability for secondary resonances', Icarus 87, 249-264.
Malhotra, R.: 1995, 'The origin of Pluto's orbit: implications for the Solar system beyond Neptune', Astron. J. 110, 420-429.
Message, P. J.: 1958, 'The search for asymmetric periodic orbits in the restricted problem of three bodies', Astron. J. 63, 443-448.
Morbidelli, A., Thomas, F. and Moons, M.: 1995, 'The resonant structure of the Kuiper Belt and the dynamics of the first five trans-Neptunian objects', Icarus 118, 322-340.
Robutel, P. and Laskar, J.: 2000 'Frequency map and global dynamics in the solar system. I: Short period dynamics of massless particles', Icarus, in press.
Torbett, M. and Smoluchowski, R.: 1980, 'Sweeping of the jovian resonances and the evolution of the asteroids', Icarus 44, 722-729.
