Kinematic Differential Geometry of a Line Trajectory in Spatial Movement-Reference-Cited by-同舟云学术

Kinematic Differential Geometry of a Line Trajectory in Spatial Movement

Published:2023-05-14 Issue:5 Volume:12 Page:472
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Almoneef Areej A.¹^ORCID,Abdel-Baky Rashad A.²

Affiliation:

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

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

Abstract

This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide a theoretical expression of inflection line congruence, which is the spatial equivalent of the inflection circle of planar kinematics. Additionally, we introduce new proofs for the Euler–Savary and Disteli formulae and thoroughly analyze their spatial equivalence.

Funder

Princess Nourah bint Abdulrahman University Researchers Supporting

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/5/472/pdf

Reference20 articles.

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3. Schaaf, J.A. (1988). Curvature Theory of line Trajectories in Spatial Kinematics. [Ph.D. Thesis, University of California].

4. Stachel, H. (1996). Instantaneous Spatial Kinematics and the Invariants of the Axodes, Institute fur Geometrie. Technical Report 34.

5. Pottman, H., and Wallner, J. (2001). Computational Line Geometry, Springer.