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On the role and the properties ofn body central configurations

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Abstract

The role central configurations play in the analysis ofn body systems is outlined. Emphasis is placed on collision orbits, expanding gravitational systems, andn body ‘zero radial velocity’ surfaces. In the second half of the paper, properties of cenral configurations are discussed. Here, emphasis is placed on describing a different approach to analyze these configurations, one which is related to the classical problem of the weightedsth mean values of a vector. This approach is illustrated by discussing the non-degeneracy of central configurations and by describing central configurations in various dimensions. This is a written version of a talk given at Oberwolfach, August, 1978.

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References

  • Easton, R.: 1971,J. Diff. Eqs. 10, 371.

    Google Scholar 

  • Marchal, C. and Saari, D. G.: 1975,Celest. Mech. 12, 115.

    Google Scholar 

  • Marchal, C. and Saari, D. G.: 1976,J. Diff. Eqs. 20, 150.

    Google Scholar 

  • Moulton, F. R.: 1910,Ann. Math 12, 1.

    Google Scholar 

  • Palmore, J.: 1976,Ann. Math. 104, 421–429.

    Google Scholar 

  • Pollard, H.: 1966,A Mathematical Introduction to Celestial Mechanics, Prentice-Hall. Now a Carus Monograph, M.A.A.

  • Pollard, H. and Saari, D. G.: 1968,Arch. Rath. Mech. Anal. 30, 263.

    Google Scholar 

  • Saari, D. G.: 1971,Trans. Amer. Math. Soc. 156, 219.

    Google Scholar 

  • Saari, D. G.: 1976,Celest. Mech. 14, 11.

    Google Scholar 

  • Smale, S.: 1970,Inventiones Math. 11, 45–64.

    Google Scholar 

  • Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.

    Google Scholar 

  • Waldvogel, J.: 1972,Celest. Mech. 5, 37.

    Google Scholar 

  • Wintner, A.: 1941,The Analytical Foundations of Celestial Mechanics, Princeton University Press.

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60201, Evanston, Illinois, USA

    Donald G. Saari

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  1. Donald G. Saari
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Additional information

proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August 1978.

This research was supported in part by an NSF Grant.

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Saari, D.G. On the role and the properties ofn body central configurations. Celestial Mechanics 21, 9–20 (1980). https://doi.org/10.1007/BF01230241

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  • DOI: https://doi.org/10.1007/BF01230241

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