Equipment including an inertial detector device provided with fastener studs enabling the inertial device to be fastened to a support frame. At least one of the fastener studs has two elements, one of which elements is fastened to the support frame and has a bearing surface that is in contact with a bearing surface of the support frame. The other element is fastened to the inertial device and has a bearing surface that is in contact with a bearing surface of the inertial device, which two elements are suspended relative to each other by means of a body made of elastically deformable material. At least one of the elements is fastened by at least one screw. The corresponding bearing surfaces is provided respectively with a centering portion and with a housing for receiving said centering portion with a fit that allows clearance of no more than 50 μm.