U.P.B. Sci. Bull., Series D, Vol. 79, Iss. 4, 2017 ISSN 1454-2358 MATHEMATICAL MODEL FOR MICROLAUNCHER, PERFORMANCES EVALUATION Teodor-Viorel CHELARU 1 , Alexandru-Iulian ONEL 2 , Tudorel Petronel AFILIPOAE 3 , Ana-Maria NECULĂESCU 4 The paper presents some aspects regarding the mathematical model and performance evaluation for a four stages microlauncher. This work uses three 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 ballistic 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 maneuver description. Keywords: mathematical model, microlauncher performances, orbital injection. Nomenclature 0  - Azimuth angle;  - Geocentric latitude;  - Geocentric longitude;  - Climb angle;  - Path track angle;  - Attack angle;   - Sideslip angle;  - Aerodynamic bank angle;  V Ω - Rotation velocity of the quasi-velocity frame; p Ω - Earth spin; D - Drag force; L - Lift force; N - Lateral force; T - Thrust force; m - Mass; t - Time; V - Velocity; z y x V V V , , - Velocity components in start frame; p p P P Z Y X O - Earth frame; L L L L Z Y X O - Local frame; S S S S Z Y X O - Start frame; r - The distance between rocket and Earth center: p R - Earth radius; g - Gravitational acceleration; e - Eccentricity; a -Semi-major axis;  - True anomaly;  - Eccentric anomaly; p - The orbit parameter. 1 Prof., University POLITEHNICA of Bucharest, Splaiul Independentei, no. 313, Bucharest, Romania, e-mail: teodor.chelaru@upb.ro 2 Eng., INCAS -National Institute for Aerospace Research “Elie Carafoli”, B-dul Iuliu Maniu 220, 061126, Bucharest, Romania, e-mail: onel.alexandru@incas.ro 3 Eng., INCAS -National Institute for Aerospace Research “Elie Carafoli”, B-dul Iuliu Maniu 220, 061126, Bucharest, Romania, e-mail: afilipoae.tudorel@incas.ro 4 Eng., INCAS -National Institute for Aerospace Research “Elie Carafoli”, B-dul Iuliu Maniu 220, 061126, Bucharest, Romania, e-mail: neculaescu.ana@incas.ro