The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space.

Abstract. The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake [13]. Using the action of the Möbius group of the unite sphere on the configuration space, in the context of a separable Hilbert space. We give a generalization of the Theorem of accessibility contained in [9] and [14] for articulated arms and snakes in a finite dimensional Hilbert space.classification: 22F50, 34C40, 34H, 53C17, 53B30, 53C50, 58B25, 93B03.