Variational Methods in the N-body Problem
The "N-body problem'' is not really one problem but rather the study
of the dynamical system written down by Newton to describe the motion of
N massive bodies attracting each other according to the laws
of gravitation. I will begin with a tour of known facts, special
solutions, and open problems. I will end by describing new results, new
special solutions, and new open problems suggested by variational methods
and Riemannian-geometrical thinking.
Animations and a number of papers can be found at http://count.ucsc.edu/~rmont/Nbdy.html.
References:
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R. Montgomery and A. Chenciner, A remarkable periodic orbit of the three-body
problem in the case of equal masses, Annals of Mathematics,
152
(2000), 881-901.
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A. Chenciner, Action minimizing solutions for the Newtonian N-body problem:
from homology to symmetry, International Congress of Mathematics, reprint
(2002), http://www.bdl.fr/Equipes/ASD/person/chenciner/chen_preprint.html.
-
W. Gordon, A minimizing property of Keplerian orbits, Am. J. Math.,
99
no. 5 (1970), 961-971.
-
H. Poincaré, Sur les solutions périodiques et le principe
de moindre action, C.R.A.S. Paris 123 (1896), 915-918.
Fall
2002 PNGS meeting