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

سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 106

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شناسه ملی سند علمی:

JR_CMCMA-2-1_006

تاریخ نمایه سازی: 10 تیر 1403

چکیده مقاله:

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.

نویسندگان

Nader Biranvand

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

Amir Hossein Salehi Shayegan

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

Hamid Ranjbar

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

Saeed Hashemi Sababe

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