Geometry of dynamic and higher-order kinematic screws

This article shows that time derivatives of twists and wrenches are indeed screws, in contrast to many classical kinematicians\´ believe. Furthermore, it is proven that the "centripetal screw" as well as the momentum of a rigid body together with all its derivatives, are also screws, and that a rigid body\´s dynamics can be geometrically expressed as a screw equation. The paper relies on a somewhat more formal treatment of the screw theory than usual, in order to clarify these "controversial" issues concerning the motion of rigid systems, and in order to make the link with the more general (and historically much richer) field of differential geometry.