Abstract
Many of the important applications of the circular planar restricted problem of three bodies involve motion in the vicinity of the unit circle, (as defined in canonical units). It is then of interest to develop simplified models which are valid in this region. These models preserve the gross characteristics of the original system but they possess simpler equations of motion.
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References
Deprit, A. and Henrard, J.: 1978, “A Manifold of Periodic Orbits”, Advances in Astronomy and Astrophysics, Vol. 6, Academic Press, New York.
Deprit, A.: 1966, “Motion in the Vicinity of the Triangular Libration Centers”, Lectures in Applied Mathematics, Vol. 6, American Mathematical Society.
Deprit, A., Henrard, J., Palmore, J. and Price, J F.: 1969, “The Trojan Manifold in the System Earth-Moon”, Mon. Not R. Astr. Soc., 137, 311–335.
Dermott, S.F. and Murray, C.D.: 1981, “The Dynamics of Tadpole and Horseshoe Orbits: I. Theory”, Icarus, 48, 1–11.
Dermott, S. F. and Murray, C.D.: 1981, “The Dynamics of Tadpole and Horseshoe Orbits: H. The Coorbital Satellites of Saturn”, Icarus, 48, 12–22.
Garfinkel, B.: 1977, “Theory of the Trojan Asteroids, Part I”, Astron. J., 82, 368–379.
Garfinkel, B.: 1975, “An Extendedldeal Resonance Problem”, Celestial Mechanics, 12, 203–214.
Garfinkel, B.: 1978, “Theory of the Trojan Asteroids. Part II, Celest Meek, 18, 259–275.
Giacaglia, G. E. O.: 1976, comments on the paper by Boris Garfinkel: “An Extended Ideal Resonance Problem”, Celestial Mechanics, 13, 515–516.
Harrington, R.S. and Seidelmann P.K.: 1981, “The Dynamics of the Saturnian Satellites 1980S 1 and 1980S3”, Icarus, 47, 97–99
Konopliv, A. S.: 1986, “Theory of Coorbital Motion”, Ph.D. dissertation, Univ. of Texas at Austin.
Salo, H. and Yoder C F.: 1988, “The Dynamics of Coorbital Satellite Systems”, A. & A., 205, 309–327
Yoder, C F., G. Colombo, S. P. Synnott, and K. A. Yoder, 1983, “Theory of Motion of Saturn’s Coorbiting Satellites”, Icarus, 53, 431–443.
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© 1999 Springer Science+Business Media Dordrecht
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Broucke, R.A. (1999). Motion Near the Unit Circle in the Three-Body Problem. 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_28
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DOI: https://doi.org/10.1007/978-94-011-4527-5_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5930-5
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