Generating hyperbolical rotation matrix for a given hyperboloid

作者：Simsek Hakan^*; Ozdemir Mustafa

来源：Linear Algebra and Its Applications, 2016, 496: 221-245.

DOI：10.1016/j.laa.2016.01.038

• Hyperbolical rotation matrix
• Hyperbolic split quaternion
• Rodrigues formula
• g-Cayley rotation matrix
• g-Householder transformation

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.

• 出版日期2016-5-1