  In this paper we show that in the $n$-body problem with harmonic potential
one can find a continuum of central configurations for $n=3$. Moreover we show
a counterexample to an interpretation of Jerry Marsden Generalized Saari's
conjecture. This will help to refine our understanding and formulation of the
Generalized Saari's conjecture, and in turn it might provide insight in how to
solve the classical Saari's conjecture for $n\geq 4$.
