Research ArticleNo Access

Kinematic geometry of hyperbolic dual spherical motions and Euler–Savary’s equation

Nadia Alluhaibi

http://orcid.org/0000-0001-7135-0559

Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia

E-mail Address: nallehaibi@kau.edu.sa

Corresponding author.

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and

R. A. Abdel-Baky

Department of Mathematics, Sciences Faculty for Girls, Jeddah University, 21352 Jeddah, Saudi Arabia

Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt

E-mail Address: rbaky@Live.com

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https://doi.org/10.1142/S0219887820500796Cited by:4 (Source: Crossref)

Abstract

In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space $𝔻_{1}^{3}$ . Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velocity, which are regarded as different forms of Euler–Savary equation form.

Keywords:

AMSC: 53A04, 53A05, 53A17

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