Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T04:05:45.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Mappings in Astrodynamics

Published online by Cambridge University Press:  07 August 2017

C. Froeschlé
C. Froeschlé*
Affiliation:
Observatoire de la Côte d'Azur, B.P. 139, F-06003 Nice Cedex, France

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We review mappings mainly devised for the study of the dynamics of comets and asteroids. An attempt of a typology according to the method used to devise the mapping and to its deterministic or stochastic character is made.

Type
Part VII - Dynamical Systems. Maps. Integrators
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 375 - 390
Copyright
Copyright © Kluwer 1992 

References

Duncan, M., Quinn, T., Tremaine, S. (1989) ‘The long-term evolution of orbits in the solar system: a mapping approach’, Icarus 82, 402–418 CrossRefGoogle Scholar
Chirikov, B.V. (1979) ‘A universal instability of many-dimensional oscilator systems’, Phys. Rep. 52, 263–379 CrossRefGoogle Scholar
Froeschlé, C. (1970) ‘A numerical study of the stochasticity of dynamical systems with two degrees of freedom’, Astron. Astrophys. 9, 15–23 Google Scholar
Froeschlé, C., Scholl, H. (1977) ‘A qualitative comparison between the circular and elliptic Sun-Jupiter-Asteroïds problem at commensurabilities’, Astron. Astrophys. 57, 33–39 Google Scholar
Froeschlé, C., Rickman, H. (1980) ‘New Monte Carlo simulations of the orbital evolution of short period comets and comparison with observations’, Astron. Astrophys. 82, 183–194 Google Scholar
Froeschlé, C., Rickman, H (1981) ‘A Monte Carlo Investigation of Jovian Perturbations on Short-Period Comet Orbits’, Icarus 46, 400–414 Google Scholar
Froeschlé, C., Rickman, H. (1988) ‘Monte Carlo modeling of cometary dynamics’, Celestial Mech. 43, 265–284 CrossRefGoogle Scholar
Froeschlé, C., Petit, J.M. (1990) ‘Polynomial approximations of Poincaré maps for Hamiltonian systems’, Astron. Astrophys. 238, 413–423 Google Scholar
Hadjidemetriou, J. (1991) ‘Mapping models for Hamiltonian systems with applications to resonant Asteroïd motion’, preprint Google Scholar
Heisler, J., Tremaine, S. (1986) ‘The influence of the galactic tidal field on the Oort comet cloud’, Icarus 65, 13–26 CrossRefGoogle Scholar
Hénon, M., Petit, J.M. (1986) ‘Series expansions for encounter-type solutions of Hill's problem’, Celestial Mech. 38, 67–100 Google Scholar
Henrard, J., Lemaître, A. (1987) ‘A perturbative treatment for the 2/1 jovian resonance’, Icarus 69, 266–279 Google Scholar
Lago, B., Cazenave, A. (1983) ‘Evolution of the cometary perihelion distance in the Oort cloud’, Icarus 53, 68–83 Google Scholar
Levinson, H.F. (1991) ‘The long-term dynamical behaviour of small bodies in the Kuiper belt’, Astron. J. Vol 102, N° 2, 787–794 Google Scholar
Lichtenberg, A.J., Lieberman, M.A. (1983), Regular and stochastic motion, Springer Verlag CrossRefGoogle Scholar
Murray, C.D., Fox, K. (1984) ‘Structure of the 3/1 jovian resonance: a comparison of numerical methods’, Icarus 59, 221–233 Google Scholar
Murray, C.D. (1986) ‘Structure of the 2/1 and 3/2 jovian resonances’, Icarus 65, 70–82 Google Scholar
Petit, J.M., Froeschlé, C. (1991) ‘Polynomial approximations of Poincaré maps for Hamiltonian systems II’ submitted to Astron. Astrophys. Google Scholar
Petrosky, T.Y., Broucke, R. (1988) ‘Area preserving mappings and deterministic chaos for nearly parabolic motions’, Celest. Mech. 42, 53–79 Google Scholar
Remy, F., Mignard, F. (1985) ‘Dynamical evolution of the Oort cloud I. A Monte Carlo simulation’, Icarus 63, 1–19 Google Scholar
Rickman, H., Froeschlé, C. (1979) ‘Orbital evolution of short-period comets treated as a Markov process’, Astron. J. 84, 1910–1917 Google Scholar
Rickman, H., Froeschlé, C. (1983) ‘A Keplerian Method to estimate Perturbations in the Restricted Three-Body Problem’, Moon and Planets 28, 69–86 Google Scholar
Rickman, H., Froeschlé, C. (1988) ‘Cometary dynamics’, Celest. Mech. 43, 243–263 Google Scholar
Rickman, H., Vaghi, S. (1976) ‘A Monte Carlo simulation of the orbital evolution of comets in the inner planetary region’, Astron. Astrophys. 51, 327–342 Google Scholar
Sagdeev, R.Z., Zaslavsky, G.M. (1987) ‘Stochasticity in the Kepler problem and a model of possible dynamics of comets in the Oort cloud’, il Nuovo Cimento, Vol 97, BN2, 119–130 CrossRefGoogle Scholar
Scholl, H., Froeschlé, C. (1974) ‘Ateroïdal motion at the 3/1 commensurability’, Astron. Astrophys. 33, 455–458 Google Scholar
Scholl, H., Froeschlé, C. (1975) ‘Asteroïdal motion at teh 5/2, 7/3 and 2/1 resonances’, Astron. Astrophys. 42, 457–463 Google Scholar
Sidlichovsky, M., Melando, B. (1986) ‘Maping for the 5/2 asteroïdal commensurability’, Bull. Astron. Inst. Czech. 37, 65–80 Google Scholar
Sidlichovsky, M. (1991) ‘Mapping for the third and fourth order asteroïdal resonances’, Proceeding of the Tokyo Symposium on ‘Celestial Mechanics’, ed. Kinoshita, H. and Yoshida, H. 38–44 Google Scholar
Varosi, F, Gebogi, C., Yorke, J.A. (1987) ‘Symplicial approximation of Poincaré maps of differential equations’, Phys. Lett. A 124, 59–64 Google Scholar
Weissman, P.R. (1982) ‘Dynamical history of the Oort cloud’ in Comets, (ed. Wilkening, L.L.), Univ. Arizona Press, Tucson, 637–658 CrossRefGoogle Scholar
Wisdom, J. (1982) ‘The origin of the Kirkwood gaps: a mapping for asteroïdal motion near the 3/1 commensurability’, Astron. J. 87, 577–593 Google Scholar
Wisdom, J. (1983) ‘Chaotic behaviour and the origin of the 3/1 Kirkwood gap’, Icarus 56, 51–74 Google Scholar
Wisdom, J. (1985) ‘A perturbative treatment of motion near the 3/1 commensurability’, Icarus 63, 272–289 Google Scholar