Computational Mathematics and Computer Modeling with Applications (CMCMA)

Three-dimensional projectile motion: analytical solution and numerical treatment of the fractional case

https://doi.org/10.48308/CMCMA.2.1.54
Volume 2, Issue 1
June 2023
Pages 54-70
Computational Mathematics and Computer Modeling with Applications (CMCMA)

Document Type : Regular paper

Authors

Nader Biranvand 1
Amir Hossein Salehi Shayegan 2
Hamid Ranjbar 1
Saeed Hashemi Sababe 3

1 Department of Mathematics, Faculty of Basic Science, Imam Ali University, Tehran, Iran

2 Mathematics Department, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran

3 Department of mathematics and statistical sciences, University of Alberta, Alberta, Canada

Abstract
This paper focuses on deriving analytical solutions for three-dimensional projectile motion and investigating numerical approaches for handling these solutions. We derive the equations of projectile motion using both classical and fractional calculus, considering scenarios with and without air resistance. We analyze the characteristics of the projectile's trajectory in both classical and fractional scenarios, providing a comparative study between them. Additionally, we propose an extrapolation method tailored to the nature of the motion equations to estimate projectile trajectories. The accuracy of our proposed method is assessed through the absolute error between exact and numerical solutions, with numerical examples provided to validate the theoretical analysis.

Keywords

Three-dimensional projectile motion
Fractional calculus
Caput\'{o}s fractional derivative
Extrapolation method
  • Receive Date 12 March 2023
  • Revise Date 05 March 2024
  • Accept Date 12 April 2024

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