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Re-Evaluating the Classical Falling Body Problem

Author

Listed:
  • Essam R. El-Zahar

    (Department of Mathematics, College of Sciences and Humanities in Al Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

  • 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
    Institute of Space Sciences, P.O. BOX MG-23, RO-077125 Magurele-Bucharest, Romania
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

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.

Suggested Citation

  • Essam R. El-Zahar & Abdelhalim Ebaid & Abdulrahman F. Aljohani & José Tenreiro Machado & Dumitru Baleanu, 2020. "Re-Evaluating the Classical Falling Body Problem," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:553-:d:343612
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