Rodrigues parameters on dual hyperbolic unit sphere

Abstract

Rodrigues parameters depend on the tangent of the half rotation angle in Euclidean space but in Dual space, dual Rodrigues parameters contain both rotation angle and distance corresponding the shortest distance between the straight lines in ℝ3. In this paper, we give Cayley's formula for the dual hyperbolic spherical motion and explain 3×3 type L-Dual skew symmetric matrices by using properties of this formula. Then, we obtain Rodrigues pa­rameters of dual Hyperbolic unit sphere and show that Rodrigues parameters contain the hyperbolic rotation angle which is being between timelike lines and distance which is the minimal Lorentzian distance between the timelike lines of .