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Motion near The Unit Circle in The Three-Body Problem

Published online by Cambridge University Press:  12 April 2016

Roger A. Broucke
Roger A. Broucke*
Affiliation:
Department of Aerospace Engineering, University of Texas, Austin, TX 78712

Extract

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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.

We will also show that several simplified models can be seen as a perturbation of a very well known simple linear system: the Clohessy-Wiltshire equations used by NASA in all their rendezvous operations. These are actually very close to the well-known Hill problem. We will thus consider the Restricted problem as a perturbed Hill or Clohessy-Wiltshire problem. We also introduce the Clohessy-Wiltshire Lagrangian in polar coordinates.

Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 281 - 290
Copyright
Copyright © Kluwer 1999

References

Deprit, A. and Henrard, J.: 1978, “A Manifold of Periodic Orbits”, Advances in Astronomy and Astrophysics, Vol. 6, Academic Press, New York.Google Scholar
Deprit, A.: 1966, “Motion in the Vicinity of the Triangular Libration Centers”, Lectures in Applied Mathematics, Vol. 6, American Mathematical Society.Google Scholar
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.CrossRefGoogle Scholar
Dermott, S.F. and Murray, C.D.: 1981, “The Dynamics of Tadpole and Horseshoe Orbits: I. Theory”, Icarus, 48, 1–11.CrossRefGoogle Scholar
Dermott, S.F. and Murray, C.D.: 1981, “The Dynamics of Tadpole and Horseshoe Orbits: II. the Coorbital Satellites of Saturn”, Icarus, 48, 12–22.CrossRefGoogle Scholar
Garfinkel, B.: 1977, “Theory of the Trojan Asteroids, Part I”, Astron. J., 82, 368–379.CrossRefGoogle Scholar
Garfinkel, B.: 1975, “An Extended Ideal Resonance Problem”, Celestial Mechanics, 12, 203–214.CrossRefGoogle Scholar
Garfinkel, B.: 1978, “Theory of the Trojan Asteroids. Part II”, Celest. Mech., 18, 259–275.CrossRefGoogle Scholar
Giacaglia, G.E.O.: 1976, comments on the paper by Boris Garfinkel: “An Extended Ideal Resonance Problem”, Celestial Mechanics, 13, 515–516.CrossRefGoogle Scholar
Harrington, R.S. and Seidelmann, P.K.: 1981, “The Dynamics of the Saturnian Satellites 1980S1 and 1980S3’, Icarus, 47, 97–99 CrossRefGoogle Scholar
Konopliv, A.S.: 1986, “Theory of Coorbital Motion”, Ph.D. dissertation, Univ. of Texas at Austin. Google Scholar
Salo, H. and Yoder, C F.: 1988, ‘The Dynamics of Coorbital Satellite Systems”, A.& A., 205, 309–327 Google Scholar
Yoder, C.F., Colombo, G., Synnott, S.P., and Yoder, K. A., 1983, “Theory of Motion of Saturn’s Coorbiting Satellites”, Icarus, 53, 431–443.CrossRefGoogle Scholar