Non-parabolic conical rotations

Çolakoğlu H. B., Öztürk İ., Özdemir M.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.420, 2023 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 420
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cam.2022.114766
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we determine non-parabolic conical motions that occur on any given ellipse or hyperbola without using affine transformations. To achieve this aim, first, we define a generalized inner product whose circle is the given ellipse or hyperbola, and then determine elliptical and hyperbolic versions of skew-symmetric and orthogonal matrices using the associated inner product. Finally, we generate elliptical and hyperbolic versions of rotation and reflection matrices using the famous Rodrigues, Cayley, and Householder transformations. For each of the generalized formulas, we give numerical examples. (c) 2022 Elsevier B.V. All rights reserved.