Tilt Angles

Abstract

Tilt angles, in contrast to Euler angles, tilt the body frame first about the line of nodes which is defined in the equator-plane of a reference frame. Thereafter only the proper rotation of the body frame takes place, through the angleabout an axis perpendicular to its own equator-plane. Thus, the two motions are clearly separated, their order is exchangeable. The tilt is described either in polar form  wheredetermines the direction of the node line and the magnitude of the tilt, or in axial form where  together determine node line and tilt by rotations about two perpendicular axes. When the tilt is visualized by geographical coordinates on a sphere,are regular except for the N- and the S-pole, whereas the  are regular, separately, on the northern and the southern hemisphere. Together the three charts provide an atlas for unlimited rotations about a fixed point. The basic relations for tilts are established for Cartesian and cylinder coordinates. Two examples demonstrate their versatility.