On the axodes of one-parameter spatial movements

Areej A. Almoneef; Rashad A. Abdel-Baky; Areej A. Almoneef; Rashad A. Abdel-Baky

doi:10.3934/math.2024483

AIMS Mathematics

2024, Volume 9, Issue 4: 9867-9883. doi: 10.3934/math.2024483

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Research article

On the axodes of one-parameter spatial movements

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

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 71516, Egypt; rbaky@live.com

Received: 28 January 2024 Revised: 23 February 2024 Accepted: 28 February 2024 Published: 12 March 2024
MSC : 53A04, 53A05, 53A17

In this treatise, several relationships are improved for the axodes of one-parameter spatial movements. Results are devised in some theorems which characterize many kinematical and geometrical properties of the movements employing the geometrical data of the stationary and movable axodes. An example illustrates the application of the formulae derived. Our findings contribute to a greater understanding of the similarities between spatial movements and axodes, with possible applications in fields such as mechanical engineering.
- Blaschke frame,
- striction curve,
- Disteli formulae
Citation: Areej A. Almoneef, Rashad A. Abdel-Baky. On the axodes of one-parameter spatial movements[J]. AIMS Mathematics, 2024, 9(4): 9867-9883. doi: 10.3934/math.2024483

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Abstract

In this treatise, several relationships are improved for the axodes of one-parameter spatial movements. Results are devised in some theorems which characterize many kinematical and geometrical properties of the movements employing the geometrical data of the stationary and movable axodes. An example illustrates the application of the formulae derived. Our findings contribute to a greater understanding of the similarities between spatial movements and axodes, with possible applications in fields such as mechanical engineering.

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