Celestial mechanics

, Volume 21, Issue 1, pp 9–20

On the role and the properties ofn body central configurations

  • Donald G. Saari


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Easton, R.: 1971,J. Diff. Eqs. 10, 371.Google Scholar
  2. Marchal, C. and Saari, D. G.: 1975,Celest. Mech. 12, 115.Google Scholar
  3. Marchal, C. and Saari, D. G.: 1976,J. Diff. Eqs. 20, 150.Google Scholar
  4. Moulton, F. R.: 1910,Ann. Math 12, 1.Google Scholar
  5. Palmore, J.: 1976,Ann. Math. 104, 421–429.Google Scholar
  6. Pollard, H.: 1966,A Mathematical Introduction to Celestial Mechanics, Prentice-Hall. Now a Carus Monograph, M.A.A.Google Scholar
  7. Pollard, H. and Saari, D. G.: 1968,Arch. Rath. Mech. Anal. 30, 263.Google Scholar
  8. Saari, D. G.: 1971,Trans. Amer. Math. Soc. 156, 219.Google Scholar
  9. Saari, D. G.: 1976,Celest. Mech. 14, 11.Google Scholar
  10. Smale, S.: 1970,Inventiones Math. 11, 45–64.Google Scholar
  11. Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.Google Scholar
  12. Waldvogel, J.: 1972,Celest. Mech. 5, 37.Google Scholar
  13. Wintner, A.: 1941,The Analytical Foundations of Celestial Mechanics, Princeton University Press.Google Scholar

Copyright information

© D. Reidel Publishing Co 1980

Authors and Affiliations

  • Donald G. Saari
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

Personalised recommendations