  The purpose of this paper is to give a simpler proof to the problem of
controllability of a Hilbert snake \cite{PeSa}. Using the action of the
M\"obius group of the unit sphere on the configuration space, in the context of
a separable Hilbert space. We give a generalization of the Theorem of
accessibility contained in \cite{Ha} and \cite{Ro} for articulated arms and
snakes in a finite dimensional Hilbert space
