The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study
| Autor: | Mona D. Aljoufi, Weam Alharbi, Essam R. El-Zahar, Abdelhalim Ebaid |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Laplace transform
General Mathematics projectile motion Projectile motion Angular velocity Rotation 01 natural sciences 010305 fluids & plasmas 0103 physical sciences Computer Science (miscellaneous) falling body problem 010301 acoustics Engineering (miscellaneous) Physical quantity Earth's rotation Mathematics lcsh:Mathematics Mathematical analysis Earth’s rotation Radius lcsh:QA1-939 Exact solutions in general relativity TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES angular velocity Computer Science::Programming Languages Falling (sensation) three dimensions |
| Zdroj: | Mathematics, Vol 8, Iss 1726, p 1726 (2020) Mathematics Volume 8 Issue 10 |
| ISSN: | 2227-7390 |
| Popis: | Very recently, the system of differential equations governing the three-dimensional falling body problem (TDFBP) has been approximately solved. The previously obtained approximate solution was based on the fact that the Earth&rsquo s rotation (ER) is quite slow and hence all high order terms of &omega in addition to the magnitude &omega 2R were neglected, where &omega is the angular velocity and R is the radius of Earth. However, it is shown in this paper that the ignorance of such magnitudes leads, in many cases, to significant errors in the estimated falling time and other physical quantities. The current results are based on obtaining the exact solutions of the full TDFBP-system and performing several comparisons with the approximate ones in the relevant literature. The obtained results are of great interest and importance, especially for other planets in the Solar System or exterior planets, in which &omega and/or &omega 2R are of considerable amounts and hence cannot be ignored. Therefore, the present analysis is valid in analyzing the TDFBP near to the surface of any spherical celestial body. |
| Databáze: | OpenAIRE |
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