One-Parameter Plane Hyperbolic Motions

• Published in: Advances in applied Clifford algebras 2008-05, Vol.18 (2), p.279-285
• Main Authors: Yüce, Salim, Kuruoğlu, Nuri
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Mathematical and Computational Physics; Mathematical Methods in Physics; Physics; Physics and Astronomy; Theoretical
• ISSN: 0188-7009; 1661-4909
• DOI: 10.1007/s00006-008-0065-z

. Müller [3], in the Euclidean plane , introduced the one parameter planar motions and obtained the relation between absolute, relative, sliding velocities (and accelerations). Also, Müller [11] provided the relation between the velocities (in the sense of Complex) under the one parameter motions in the Complex plane . Ergin [7] considering the Lorentzian plane , instead of the Euclidean plane , and introduced the one-parameter planar motion in the Lorentzian plane and also gave the relations between both the velocities and accelerations. In analogy with the Complex numbers, a system of hyperbolic numbers can be introduced: . Complex numbers are related to the Euclidean geometry, the hyperbolic system of numbers are related to the pseudo-Euclidean plane geometry (space-time geometry), [5,15]. In this paper, in analogy with Complex motions as given by Müller [11], one parameter motions in the hyperbolic plane are defined. Also the relations between absolute, relative, sliding velocities (and accelerations) and pole curves are discussed.