Relative equilibria and the virial theorem

Details Relative equilibria and the virial theorem Relative equilibria and the virial theorem

Feb 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19..167p&link_type=abstract

Celestial Mechanics, vol. 19, Feb. 1979, p. 167-171.

Physics

7

Many Body Problem, Virial Theorem, Energy Methods, Kinetic Energy, Potential Energy

Scientific paper

Saari's conjecture can be stated as follows: Let (x(t), v(t)) be a solution of the Newtonian n-body problem for some interval of time over which the moment of inertia of the mass system with respect to the center of mass is constant. Then (x(t), v(t)) is a solution of relative equilibrium. This conjecture is proved by invoking critical point theory. As a consequence of the proof of Saari's conjecture, it is shown that any solution of the n-body problem for which 2K(t) = -V(t) holds is a rigid motion, where K(t) is the kinetic energy and V(t) the potential.

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