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On Elliptical Motions on a General Ellipsoid

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Abstract

In this paper, we determine elliptical motions that occur on any given ellipsoid in 3D space without using affine transformations. To this end, first, we define the generalized Euclidean inner product whose sphere is the given ellipsoid, and determine skew symmetric matrices and the generalized vector product related to the 3D generalized Euclidean inner product space. Finally, we generate elliptical rotation matrices in 3D generalized Euclidean space using the famous Rodrigues, Cayley, and Householder methods. The formulas and results obtained are supported with numerical examples. We also give an algorithm for generalized elliptical rotation.

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Authors and Affiliations

  1. Department of Computer Technologies, Akdeniz University, Antalya, Turkey

    Harun Barış Çolakoğlu & Mustafa Özdemir

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  1. Harun Barış Çolakoğlu
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  2. Mustafa Özdemir
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These authors contributed equally to this work. Two authors wrote and reviewed the manuscript.

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Correspondence to Harun Barış Çolakoğlu.

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Çolakoğlu, H.B., Özdemir, M. On Elliptical Motions on a General Ellipsoid. Mediterr. J. Math. 20, 130 (2023). https://doi.org/10.1007/s00009-023-02353-x

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  • DOI: https://doi.org/10.1007/s00009-023-02353-x

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