Abstract - The paper purpose is to present some aspects regarding the calculus model and technical solutions for multistage sounding rockets used to test spatial equipment and scientific measurements. The calculus methodology consists in numerical simulation of sounding rocket evolution for different start conditions. The rocket model presented will be with six DOF and variable mass. At this item, as novelty of the work we will use simultaneously the rotation angles and the attitude angles for describing the kinematical equations of the movement. The results analyzed will be the flight parameters and the ballistic performances. The conclusions will focus technical possibilities to realize sounding multi-stage rocket recycling military rocket engines. Keywords— Multi-stage, Mathematic model, Sounding rocket, Simulation, Rotation angles NOMENCLATURE α - Attack angle (tangent definition); β - Sideslip angle (tangent definition); p β - Azimuth angle; p λ - Geocentric latitude; ψ - Azimuth angle; θ - Inclination angle; φ - Bank angle; ρ - Air density; Ω - Body angular velocity; p Ω Earth spin: E C B A , , , - Inertia moments; A z A y A x C C C ; ; - Aerodynamic coefficients of force in the mobile frame; A n A m A l C C C ; ; , - Aerodynamic coefficients of momentum in the mobile frame; T z T y T x C C C ; ; - Thrust coefficients in the mobile frame; T n T m T l C C C ; ; - Thrust momentum coefficients in the mobile frame. ζ η ξ , , - Rotation angles * University POLITEHNICA of Bucharest, Splaiul Independentei 313, Postal code 060032, Bucharest, Romania. e-mail: t.v.chelaru@rom-arm.ro † Military Technical Academy, Bulevardul George Cosbuc nr. 81-83, Sector 5, postal code 050141, Bucharest, Romania, e-mail: barbucr@mta.ro S V F 2 2 0 ρ = - Reference aerodynamic force; l F H A o 0 = - Reference aerodynamic couple; 0 T - Reference thrust force l T H T o 0 = Reference couple thrust l - Reference length; m - Mass; i m - Initial mass f m - Final mass r q p , , - Angular velocity components along the axes of mobile frame; S - Reference area; T - Thrust; Σ I - Total impulse; t - Time; V - Velocity; w v u , , - Rocket velocity components in mobile frame; zp yp xp V V V Velocity components in Earth frame; p p p Z Y OX - Normal Earth-fixed frame; Oxyz – Body frame (mobile frame); p p p z y x - Mobile coordinates in Earth-fixed frame; r - The distance between rocket and Earth center: p R - Earth radius: I. INTRODUCTION t is indisputable that today, the spatial program involves many collateral activities, like preliminary tests for equipment and qualifications. It is well known that those auxiliary activities suppose huge technical and financial effort and this increases the total cost for any space program. Starting from this idea, the paper proposes an economical solution for preliminary tests using small multistage sounding rockets by recycling military rocket engines. The sounding rockets are commonly used to take readings or carry instruments from 50 to 150 km above the surface of the Earth, the altitude generally between weather balloons and satellites. The region above the maximum altitude for balloons is about 40 km and the minimum for satellites is approximately 120 km. A common sounding rocket consists of a solid-fuel rocket motor and a payload. The freefall part of the flight is an elliptic trajectory Mathematical model for sounding rockets, using attitude and rotation angles Teodor-Viorel Chelaru * , Cristian Barbu † I Issue 2, Volume 3, 2009 35 INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND INFORMATICS