Re-Evaluating the Classical Falling Body Problem

Essam R. El-Zahar, Abdelhalim Ebaid, Abdulrahman F. Aljohani, José Tenreiro Machado and Dumitru Baleanu
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Essam R. El-Zahar: Department of Mathematics, College of Sciences and Humanities in Al Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
Abdelhalim Ebaid: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Abdulrahman F. Aljohani: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
José Tenreiro Machado: Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey

Mathematics, 2020, vol. 8, issue 4, 1-10

Abstract: This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.

Keywords: falling body problem; angular velocity; projectile motion; three dimensions; Earth’s rotation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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