One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

Areej A. Almoneef and Rashad A. Abdel-Baky ()
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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

Mathematics, 2023, vol. 11, issue 17, 1-13

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.

Keywords: Serret–Frenet formulae; rectifying curve; helices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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