Elliptic motion on dual hyperbolic unit sphere H∼02

Planar and spherical elliptic motions had been introduced by Karger and Novák [A. Karger, J. Novák, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York, London, 1985]. Also, a dual spherical elliptic motion has been defined by Yapar [Z. Yapar, Spatial conchoidal and elliptic motions, Mechanism and Machine Theory 27 (1) (1992) 75–91]. In this paper, we define the elliptic motion on a dual hyperbolic unit sphere H∼02 in the dual Lorentzian space D13 with dual signature (+, +, −) and carry the results to the Lorentzian line space IR13 by means of Study’s mapping.