Zermelo's navigation problem for some special surfaces of rotation

Yanlin Li; Piscoran Laurian-Ioan; Lamia Saeed Alqahtani; Ali H. Alkhaldi; Akram Ali; Yanlin Li; Piscoran Laurian-Ioan; Lamia Saeed Alqahtani; Ali H. Alkhaldi; Akram Ali

doi:10.3934/math.2023833

AIMS Mathematics

2023, Volume 8, Issue 7: 16278-16290. doi: 10.3934/math.2023833

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Zermelo's navigation problem for some special surfaces of rotation

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
North University Center of Baia Mare Technical University of Cluj Napoca Department of Mathematics and Computer Science, Victoriei 76, 430122 Baia Mare, Romania
3.
Department of Mathematics, King Abdulaziz University, 21589 Jeddah, Saudi Arabia
4.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Received: 10 February 2023 Revised: 31 March 2023 Accepted: 05 April 2023 Published: 08 May 2023
MSC : Primary 53C60; Secondary 53B40

In this paper, we investigate Zermelo's navigation problem for some special rotation surfaces. In this respect, we find some Randers-type metrics for these rotation surfaces. Furthermore, we get the H-distortion for the metric induced by surfaces.
- Zermelo's problem,
- Frobenius norm
Citation: Yanlin Li, Piscoran Laurian-Ioan, Lamia Saeed Alqahtani, Ali H. Alkhaldi, Akram Ali. Zermelo's navigation problem for some special surfaces of rotation[J]. AIMS Mathematics, 2023, 8(7): 16278-16290. doi: 10.3934/math.2023833

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Abstract

In this paper, we investigate Zermelo's navigation problem for some special rotation surfaces. In this respect, we find some Randers-type metrics for these rotation surfaces. Furthermore, we get the H-distortion for the metric induced by surfaces.

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