Journal of Applied Mathematics
Volume 2011 (2011), Article ID 871304, 19 pages
http://dx.doi.org/10.1155/2011/871304
Research Article

Air Drag Effects on the Missile Trajectories

F. A. Abd El-Salam1,2

1Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2Department of Astronomy, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 24 May 2011; Accepted 3 August 2011

Academic Editor: Michela Redivo-Zaglia

Copyright © 2011 F. A. Abd El-Salam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The equations of motion of a missile under the air drag effects are constructed. The modified TD88 is surveyed. Using Lagrange's planetary equations in Gauss form, the perturbations, due to the air drag in the orbital elements, are computed between the eccentric anomalies of the burn out and the reentry points [ 𝐸 𝑏 𝑜 , 2 𝜋 − 𝐸 𝑏 𝑜 ], respectively. The range equation is expressed as an infinite series in terms of the eccentricity e and the eccentric anomaly E. The different errors in the missile-free range due to the drag perturbations in the missile trajectory are obtained.