One-parameter Lorentzian spatial kinematics and Disteli's formulae

Awatif Al-Jedani; Rashad A. Abdel-Baky; Awatif Al-Jedani; Rashad A. Abdel-Baky

doi:10.3934/math.20231029

AIMS Mathematics

2023, Volume 8, Issue 9: 20187-20200. doi: 10.3934/math.20231029

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One-parameter Lorentzian spatial kinematics and Disteli's formulae

Awatif Al-Jedani ¹,
Rashad A. Abdel-Baky ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt

Received: 22 March 2023 Revised: 30 May 2023 Accepted: 04 June 2023 Published: 19 June 2023
MSC : 53A04, 53A05, 53A17

In this paper, based on the E. Study map, clear terms are offered for the differential equations of one-parameter Lorentzian spatial kinematics that are coordinate system-independent. This cancels the request of demanding coordinate transformations that are typically required in the determination of the canonical systems. With the suggested technique, new proofs of the Disteli formulae of a spacelike line trajectory are instantly gained and their spatial equivalents are studied in detail. As a consequence, we address the kinematic geometry of a point trajectory for the one-parameter Lorentzian spherical and planar movements.
- spacelike axodes,
- planar movement,
- inflection circle
Citation: Awatif Al-Jedani, Rashad A. Abdel-Baky. One-parameter Lorentzian spatial kinematics and Disteli's formulae[J]. AIMS Mathematics, 2023, 8(9): 20187-20200. doi: 10.3934/math.20231029

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Abstract

In this paper, based on the E. Study map, clear terms are offered for the differential equations of one-parameter Lorentzian spatial kinematics that are coordinate system-independent. This cancels the request of demanding coordinate transformations that are typically required in the determination of the canonical systems. With the suggested technique, new proofs of the Disteli formulae of a spacelike line trajectory are instantly gained and their spatial equivalents are studied in detail. As a consequence, we address the kinematic geometry of a point trajectory for the one-parameter Lorentzian spherical and planar movements.

References

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