Article details

Title: A Mathematical Model for Computing the Trajectories of Rockets in a Resistant Medium Taking into Account the Earth’s Rotation. Part 1: The Vector Equation of Rocket’s Motion with Respect to the Earth. The Position of the Rocket with Respect to an Earth-Linked Geocentric Frame
Author(s): Florentin Moraru   LaurenÅ£iu Moraru   Bogdan Scobeniuc         

Abstract: This paper establishes the system of ordinary equations of the trajectory of a rocket with respect to the Earth, while taking into account the aerodynamic drag, the weight, and the Earth’s rotation and curvature. The local latitude and the longitude during the flight, which implicitly appears in the expressions of the forces acting upon the rocket, are determined as well. The mathematical model obtained is formalized for ballistics. This system of equations can also be used for the calculation of the trajectory of an active-reactive projectile, and also, with some adjustments, for the calculation of the trajectory of an aerospace vehicle.

Keywords: rocket, Earth’s rotation, trajectory, rocket’s latitude and longitude.

[1] H. MOLITZ, R. STROBEL – Exterior Ballistics, Springer-Verlag, Berlin, Germany, 1963 (in German)
[2] F. MORARU – Exterior Ballistics and Rocket’s Flight Dynamics, Military Academy Publishing House, Bucharest, Romania, 1973 (in Romanian)
[3] F. MORARU – Handbook of Exterior Ballistics, Military Publishing House, Bucharest, Romania, 1976 (in Romanian)
[4] F. MORARU – Chapters of Numerical Analysis: Applications in Ballistics and Flight Dynamics, 2nd Edition, Military Technical Academy Publishing House, Bucharest, Romania, 2001 (in Romanian)
[5] M.M. NIŢĂ, D.Şt. ANDREESCU – The Guided and Unguided Rocket’s Flight, Military Publishing House, Bucharest, Romania, 1964 (in Romanian)
[6] V. VÂLCOVICI, Şt. BĂLAN, R. VOINEA – Theoretical Mechanics, Technical Publishing House, Bucharest, Romania, 1963 (in Romanian)