The dual exponential mapping on dual rotations

Abstract

Dual numbers are introduced by Clifford in the mid-nineteenth century and they are systematically applied to kinematics by Study (1903) and Kotelnikov (1895). Any point on the dual unit sphere (DUS) corresponds to a straight line in QUOTE (real three space), and vice versa. By this way, there is a one to one correspondence between the dual curves on DUS and the one parameter rigid body motions in QUOTE . Using Cayley Mapping (McCarthy, 1990) we get a relation between the dual rotation matrices and the dual skew symmetric matrices. In this paper, this relation is given by the exponential mapping which can be called the dual exponential mapping. Keywords: Kinematics, study mapping, cayley mapping, dual exponential mapping.