Statistics – Computation
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aipc.1043..101d&link_type=abstract
EXPLORING THE SOLAR SYSTEM AND THE UNIVERSE. AIP Conference Proceedings, Volume 1043, pp. 101-111 (2008).
Statistics
Computation
Celestial Mechanics, Newtonian Mechanics, Rotational Kinematics, Computational Methods In Continuum Mechanics, Lagrangian And Hamiltonian Mechanics, Energy Conservation
Scientific paper
In 1969, D. Saari conjectured that the only solutions of the Newtonian n-body problem that have constant moment of inertia are relative equilibria. For n = 3, there is a computer assisted proof of this conjecture given by R. Moeckel in 2005, [10]. The collinear case was solved the same year by F. Diacu, E. Pérez-Chavela, and M. Santoprete, [4], All the other cases are open. Denoting by U the potential energy, Saari's homographic conjecture states that if along an orbit of the n-body problem IU2 is constant, then the orbit is a homographic solution, i.e. a solution whose initial configuration remains similar to itself. In this paper, we discuss both conjectures and survey the proof of the latter for a large set of initial data. This survey follows our previous paper on this subject, [5].
Diacu Florin
Fujiwara Toshiaki
Pérez-Chavela Ernesto
Santoprete Manuele
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