The present paper deals with the force function´s transformation in the general threebody problem in Jacobi´s coordinates. In this transformation we make use of Rose´s idea about the traslation of the spherical functions in Quantum Electrodynamics.
An analytical averaging theory founded on the elliptic restricted three-body problem and valid for libration motions shows that there are forbidden intervals in the distribution of the mean semi-major axes at the resonance (p+1) : p. The actual asteroids may cross these gaps but they cannot remain there. Some 15 of the presently known Hildas are in the gap and some of them may cross it completely. The Griquas are presently at the left of the gap but some of them periodically cross the gap.