Abstract
We present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear. The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.
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References
Ferraz-Mello, S.: 1997, A Symplectic Mapping approachto the study of the Stochasticity of asteroidal Resonances, Cel. Mec. Dyn. Astr. 65, 421–437.
Ferraz-Mello, S. and Michtchenko, T.A.: 1997, Orbital evolution of Asteroids in the Hecuba Gap, in R. Dvorak and J. henrard (eds.) The Dynamical behaviour of our Planetary System, Kluwer Acad. Publ., 377–384.
Ferraz-Mello, S., Michtchenko, T.A., Nesvorny, D., Roig, F. and Simula, A.: 1998a, The depletion of the Hecuba Gap vs. the long-lasting Hilda group, Planetary and Space Science, in press.
Ferraz-Mello, S., Michtchenko, and Roig, F.: 1998b, The determinant role of Jupiter’s Great Inequality in the depletion of the Hecuba Gap, Astron. J. 116, 1491–1500.
Franklin, F.: 1994, En examination of the relation between Chaotic Orbits and the Kirkwood Gap at the 2:1 Resonance, Icarus 107, 1890–1899.
Gallardo, T. and Ferraz-Mello, S.: 1998, Understanding libration via time-frequency analysis Astron J. 113, 863–870.
Hadjidemetriou, J.D.: 1993, Asteroid Motion near the 3:1 Resonance, Cel. Mec. Dyn. Astr. 56, 563–599.
Hadjidemetriou, J.D. and Lemaitre, A.: 1997, Asteroid motion near the 2:1 resonance: a symplectic mapping approach, in R. Dvorak and J. Henrard (eds.) The Dynamical Behaviour of our Planetary System, Kluwer Acad. Publ., 277–290.
Henrard, J. and Lemaitre, A.: 1987, A Perturbative Treatment of the 2/1 Jovian Resonance, Icarus 69, 266–279.
Henrard, J., Watanabe, N. and Moons, M.: 1995, A bridge between Secondary and Secular Resonances inside the Hecuba Gap, Icarus 115, 336–346.
Lemaitre, A. and Henrard, J.: 1990, On the Origin of Chaotic Behaviour in the 2/1 Kirkwood Gap, Icarus 83, 391–409.
Michtchenko, T.A. and Ferraz-Mello, S.: 1997, Escape of Asteroids from the Hecuba Gap, Planetary and Space Science 45, 1587–1593.
Moons, M. and Morbidelli, A.: 1993, The main Mean Motion Commensurabilities in the Planar Circular and Elliptic Problem, Cel. Mec. Dyn. Astr. 57, 99–108.
Moons, M. and Morbidelli, A.: 1995, Secular Resonances in Mean Motion Commensurabilities: the 4/3, 3/1, 5/2 and 7/3 cases, Icarus 114, 33–50.
Moons, M., Morbidelli, A. and Migliorini, F.: 1998, Dynamical Structure of the 2/1 Commensurability with Jupiter and the origin of the Resonant Asteroids, Icarus ***
Morbidelli, A.: 1996, On the Kirkwood Gap at the 2/1 Commensurability with Jupiter: numerical results, Astron. J. 111, 2453–2461.
Morbidelli, A. and Moons, M.: 1993, Secular Resonances in Mean Motion Commensurabilities: the 2/1 and 3/2 cases, Icarus 102, 316–332.
Nesvorny, D. and Ferraz-Mello, S.: 1997, On the asteroidal population of the first-order resonances, Icarus 130, 247–258.
Šidlichovský M.: 1988, On the Origin of 5/2 Kirkwood Gap in Proceedings of the LAU Colloq. 96, The Few Body Problem, Turku, (ed. Valtonen M.), p. 117.
Šidlichovský M.: 1991, Tables of the Disturbing Function for Resonant Asteroids, Bull. Astron. Inst Czech. 42, 116–123.
Šidlichovský M.: 1992, Mapping For the Asteroidal Resonances, Astron. Astrophys. 259, 341–348.
Wisdom, J.: 1982, The origin of the Kirkwood Gaps, Astron. J. 87, 577–593.
Wisdom, J.: 1983, Chaotic Behaviour and the Origin of the 3/1 Kirkwood Gap, Icarus 56, 51–74.
Wisdom, J.: 1985, A Perturbative Treatment of Motion Near the 3/1 Commensurability, Icarus 63, 272–289.
Yoshikawa, M.: 1989, A survey of the Motion of Asteroids in Commensurabilities with Jupiter, Astron. Astrophys. 213, 436–458.
Yoshikawa, M.: 1991, Motions of Asteroids at the Kirkwood Gaps. II. On the 5:2, 7:3 and 2:1 Resonances with Jupiter, Icarus 92, 94–117.
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Hadjidemetriou, J.D. (1999). A Symplectic Mapping Model as a Tool to Understand the Dynamics of 2/1 Resonant Asteroid Motion. In: Henrard, J., Ferraz-Mello, S. (eds) Impact of Modern Dynamics in Astronomy. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4527-5_7
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DOI: https://doi.org/10.1007/978-94-011-4527-5_7
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