Saari’s conjecture for the collinear $n$-body problem
Saari’s conjecture for the collinear $n$-body problem
In 1970 Don Saari conjectured that the only solutions of the Newtonian $n$-body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture in the collinear case for any potential that involves only the mutual distances. Furthermore, in the case of homogeneous potentials, we show …