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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2010 / Volume: 59 Issue: 2

UNIT DUAL QUATERNIONS AND ARCS

Hesna Kabadayı
Yusuf Yaylı
Pages
—
Publication Date
2010-08-01
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AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper we obtain sine and cosine rules for dual spherical triangle on the dual unit sphere S^2 by representing great circle arcs by dual quatrenions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we obtain sine and cosine rules for dual spherical triangle on the dual unit sphere S^2 by representing great circle arcs by dual quatrenions.
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Key Findings & Data:In this paper we obtain sine and cosine rules for dual spherical triangle on the dual unit sphere S^2 by representing great circle arcs by dual quatrenions.
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Conclusion & Impact:In this paper we obtain sine and cosine rules for dual spherical triangle on the dual unit sphere S^2 by representing great circle arcs by dual quatrenions.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:sine rule · cosine rule · dual spherical triangle

Abstract

In this paper we obtain sine and cosine rules for dual spherical triangle on the dual unit sphere S^2 by representing great circle arcs by dual quatrenions.

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Cite This Article

Kabadayı, H., Yaylı, Y. (2010). UNIT DUAL QUATERNIONS AND ARCS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 59 Issue: 2. https://doi.org/10.1501/Commua1_0000000661

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References (6)

  1. J. P. Ward, Quaternions and Cayley Numbers, Kluwer Academic Publisher, 1997.
  2. G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantenaous, spatial kinematics, Mechanism and Machine Theory, 1976 vol. 11, pp. 141-156.
  3. A. F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, Berlin 1983.
  4. H. H. U¼gurlu and H. Gündo¼gan, The cosine hyperbolic and sine hyperbolic rules for dual hyperbolic spherical trigonometry, Mathematical and Computational Applications, Vol. 5, No. 3, 185-190, 2000.
  5. M. Kazaz, H.H. U¼gurlu, A. Özdemir, The cosine rule II for a spherical triangle on the dual unit sphere S2, Math. Comput. Appl. 10 (2005), no.3, 313-320. Current address: Ankara University, Faculty of Sciences, Dept.of Mathematics, Ankara, TURKEY E-mail address: [email protected], [email protected] URL: http://communications.science.ankara.edu.tr
  6. M. Kazaz, H.H. U¼gurlu, A. Özdemir, The cosine rule II for a spherical triangle on the dual unit sphere S2, Math. Comput. Appl. 10 (2005), no.3, 313-320. Current address: Ankara University, Faculty of Sciences, Dept.of Mathematics, Ankara, TURKEY E-mail address: [email protected], [email protected] URL: http://communications.science.ankara.edu.tr