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One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

Author

Listed:
  • Areej A. Almoneef

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Rashad A. Abdel-Baky

    (Department of Mathematics, Faculty of Science, University of Assiut, Asiut 71516, Egypt)

Abstract

In this paper, based on the E. Study map, direct appearances were sophisticated for one-parameter hyperbolic dual spherical locomotions and invariants of the axodes. With the suggested technique, the Disteli formulae for the axodes were acquired and the correlations through kinematic geometry of a timelike line trajectory were provided. Then, a ruled analogy of the curvature circle of a curve in planar locomotions was expanded into generic spatial locomotions. Lastly, we present new hyperbolic proofs for the Euler–Savary and Disteli formulae.

Suggested Citation

  • Areej A. Almoneef & Rashad A. Abdel-Baky, 2023. "One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode," Mathematics, MDPI, vol. 11(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3749-:d:1230058
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