Abstract
A review is presented of periodic orbits which are of interest to Dynamical Astronomy and their relation to actual systems is given. In particular, we review periodic orbits in planetary systems with two or more planets, in the asteroid system, in stellar systems and in the motion of a star in various types of galaxies. Most systems are close to integrable ones and the properties of the existing families of periodic orbits can be found by studying the continuation of the families of periodic orbits of the unperturbed system. The evolution of the stability properties from the unperturbed to the actual system is also studied and in this way the relation between resonance and instability or nonintegrability and instability is revealed. The qualitative differences which appear as the number of degrees of freedom is increased, and the factors which affect the stability are analyzed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aa, Els Van der: 1983, Celes. Meen. 31, 163.
Aa, Els Van der and de Winkel, M.: 1987, Univ. of Utrecht preprint.
Arnold, V.I. and Avez, A.: 1968, “Ergodic Problems of Classical Mechanics”, Benjamin, Ch.4.
Athanassoula, E., Beinayne, B., Martinet, L., Phenniger, D.: 1983, Astron. Astrophys. 127, 349.
Barbanis, B.: 1984, Celes. Mech. 33, 385.
Barbanis, B.: 1985, Celes. Mech. 36 , 257.
Broucke, R.: 1975, Celes. Mech. 12, 439.
Brumberg, V. A. and Kovalevsky, J.: 1986, Celes. Mech. 39,13.
Contopoulos, G.: 1970, Astron. J. 75, 96.
Contopoulos, G.: 1976, in V. Szebehely and E.T. Tapley (eds) “Long Time Predictions in Dynamics”, D. Reidel Publ. Co., p.43.
Contopoulos, G.: 1980, Astron. Astrophys. 81, 148.
Contopoulos, G.: 1981a, Celes. Mech. 24, 355.
Contopoulos, G.: 1981b, Astron. Astrophys. 102, 265.
Contopoulos, G.: 1983a, Celes. Mech. 31 193.
Contopoulos, G.: 1983b, Physica 8D, 142.
Contopoulos, G.: 1983c, Astron. Astrophys. 117, 89.
Contopoulos, G.: 1985, in R. Bucher et. al. (eds) “Chaos in Astrophysics”, D. Reidel Publ. Co., p.259.
Contopoulos, G.: 1986a, Celes. Mech. 38, 1.
Contopoulos, G.: 1986b, Astron. Astrophys. 161, 244.
Contopoulos, G. and Michaelidis, P.: 1980, Celes.Mech. 22, 403
Contopoulos, G. and Papayancpoulos, Th.: 1980, Mon. Not. R. A.S. 201, 303.
Contopoulos, G. and Magnenat, P.: 1985, Celes. Mech. 37, 387.
Grigorelis, F.: 1987, Doctor’s Thesis, Univ. of Thessaloniki.
Hadjidemetriou J.D.: 1975a, Celes. Mech. 12, 155.
Hadjidemetriou, J.D.: 1975b, Celes. Mech. 12 , 255.
Hadjidemetriou, J.D.: 1976a, Astrophys. Space Sci 40, 201.
Hadjidemetriou, J.D.: 1976b, in V. Szebehely (ed) “Long Time Predictions in Dynamics”, D. Reidel Publ. Co., p.223.
Hadjidemetriou, J.D.: 1977, Celes. Mech. 16, 61.
Hadjidemetriou, J.D.: 1981, Celes. Mech. 23, 277.
Hadjidemetriou, J.D.: 1982, Celes. Mech. 27, 305.
Hadjidemetriou, J.D.: 1984, Celes. Mech. 34 , 379.
Hadjidemetriou, J.D.: 1985a, in V. Szebehely (ed.) “Stability of the Solar System and its Minor Natural and Artificial Bodies”, D. Reidel Publ. Co., p.213.
Hadjdiemetriou, J.D.: 1985b, in S. Ferraz-Mello and W. Sessin (eds) “Resonances in the Motion of Planets, Satellites and Asteroids”, Univ. de Sao Paulo, p.1.
Hadjidemetriou, J.D. and Michalodimitrakis, M.: 1978, in V. Szebehely (ed) “Dynamics of planets and Satellites and Theories of their Motion”, D. Reidel Publ. Co., p.263.
Hadjidemetriou, J.D. and Michalodimitrakis, M.: 1981, Astron. Astrophys. 93, 204.
Hadjidemetriou, J.D. and Ichtiaroglou, S.: 1984, Astron. Astrophys. 131, 20.
Hénon, M.: 1974, Celes. Mech. 10, 375.
Knowk, J. H. and Nacozy, E.: 1985, Celes. Mech. 35, 289.
Magnenat, P.: 1982, Celes. Mech. 28, 319.
Michalodimitrakis, M. and Terzides, C: 1985a, Astrophys. Space. Sci 114 , 191.
Michalodimitrakis, M. and Terzides, C: 1985b, Astron. Astrophys. 150, 83.
Michalodimitrakis, M. and Terzides, C: 1985c, Astrophys. Space Sci. 115, 377.
Michalodimitrakis, M. and Terzides, C: 1986, Astrophys. Space Sci. 124 , 289.
Papayanopoulos, Th. and Petrou, M.: 1983, Astron. Astrophys. 119,21.
Pfenniger, D.: 1984, Astron. Astrophys. 134, 373.
Roy, A. E.: 1982, “Orbital Motion” (2nd ed.), Adam Hilger, London.
Scidelman, R.K.: 1986, Celes. Mech. 39, 141.
Standish, E.M.: 1972, Astron. Astrophys. 21, 185.
Szebehely, V. 1967, “Theory of Orbits”, Academic Press, New York.
Szebehely, V.: 1972, Celes. Mech. 6, 84.
Van Albada, T. S. and Sanders, R.H.: 1985, Mon. Not. R.A.S. 201, 303.
Yakubovich, V. and Starzhinskii, V.M.: 1975, “Linar Differential Equations with Periodic Coefficients”, Vol 1, Halsted Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Kluwer Academic Publishers
About this paper
Cite this paper
Hadjidemetriou, J.D. (1988). Periodic Orbits and Stability. In: Valtonen, M.J. (eds) The Few Body Problem. Astrophysics and Space Science Library, vol 140. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2917-3_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-2917-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7813-9
Online ISBN: 978-94-009-2917-3
eBook Packages: Springer Book Archive