Performances Evaluation for Microlauncher, Mathematical Model

Abstract

Abstract-The paper presents some aspects regarding the mathematical model and performance evaluation of a three stages microlauncher with a payload up to 50 kg. This work uses two separate models dedicated for each flight phase. For the ascending phase, we will use a three degrees of freedom model in quasi-velocity frame. For the orbital phase we will use a Kepler model, and for the orbital injection a Gauss perturbing model. The results analyzed will be in quasi-velocity frame but also some orbital parameters will be presented. Using these models, the microlauncher performances will be evaluated. The novelty of the paper consists in orbital injection approach, with optimal maneuvers description. IndexTerms-Mathematical model, microlauncher performances, orbital injection, optimal maneuvers.

Nonlinear Model for Micro-Launcher Attitude Control

“…Because the translational equations were presented in paper [1], in 3DOF model, we will briefly review the translational equations and focus on rotational equations.…”

“…Summarizing the papers [1], [9] to obtain the translational equation in quasi-velocity frame, we start from vector equation:…”

“…The present work is a continuation of the paper [1] where, using three degree of freedom (3DOF) model, based on translational equation, the ascending phase of the micro-launcher (ML) was optimized and performance for Low Earth Orbit was evaluated. The present work proposes to develop the ML model adding the equations of the movement around center of mass (dynamic and kinematic) and the equations of the aerodynamic angles to obtain a six degree of freedom (6DOF) model.…”

“…The work is focused on linear form of motion equation, in particular the longitudinal plane. A practical approach is propose in work [5], where the main phases of ascension are defined, which then would help us with the 3DOF model approach of this paper [1]. Work [6], dedicated to reentry vehicle, proposed the use of no inertial geographical frame for express attitude of the vehicle, an idea that we will develop in this paper for the orbital injection phases.…”

Flexible Model for Miro-launcher Dynamics

“….0,02. (36)If we retain the first n frequency, then from (35) angular velocity in the oscillation plane will be affected by the sum of the deviations introduced by the elastic oscillations: * = + ∆ ; * = + ∆ (32) where ψ , q are the actual values, * * ψ , q are the measured values and ∆ , ∆ are the influence of the flexible oscillations of the launcher structure in yaw.∆ = ∑ =1 ; ∆ = ∑ =1(33)3 Input data for micro-launcher modelThe main input data used are extracted from paper[8]. InFig.…”