Generating hyperbolical rotation matrix for a given hyperboloid

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Şimşek H., ÖZDEMİR M.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.496, pp.221-245, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 496
  • Publication Date: 2016
  • Doi Number: 10.1016/j.laa.2016.01.038
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.221-245
  • Keywords: Hyperbolical rotation matrix, Hyperbolic split quaternion, Rodrigues formula, g-Cayley rotation matrix, g-Householder transformation, QUATERNIONS, SPACE, TIME
  • Akdeniz University Affiliated: Yes


Hyperbolic rotation is hyperbolically the motion of a smooth object on general hyperboloids given by -a(1)x(2)+a(2)y(2)+a(3)z(2) = +/-lambda, lambda is an element of R+. In this paper, we investigate the hyperbolical rotation matrices in order to get the motion of a point about a fixed point or axis on the general hyperboloids by defining the Lorentzian Scalar Product Space R-a1a2a3(2,1) such that the general hyperboloids are the pseudo-spheres of R-a1a2a3(2,1). We adapt the Rodrigues, Cayley, and Householder methods to R-a1a2a3(2,1) and define hyperbolic split quaternions to obtain an hyperbolical rotation matrix. (C) 2016 Elsevier Inc. All rights reserved.