Attitude Dynamics of ESMO Satellite: Mass Expulsion Torques and Propellant Slosh Model

Stefania Soldini, Franco Bernelli-Zazzera, Massimiliano Vasile


The European Student Moon Orbiter (ESMO) was the first European student mission to the Moon and the fourth mission within ESA (European Space Agency) Education Satellite Programme. The purpose of this mission was to place the spacecraft on a polar orbit around the Moon, return new data by acquiring surface images of the Moon South Pole and test new technologies.
This paper deals with the Newton and Euler's dynamic equations of ESMO, where the mathematical formulation of its internal dynamics were the major subject of study. Indeed, it was designed the internal (non-environmental) disturbances of the spacecraft, by focusing on the mass expulsion torques and, primarily, on the propellant sloshing effect. Moreover, the reaction wheel's dynamics were included in the equations of motion since they are part of the actuators devices, and their modelling makes the system suitable for adding the control law. Firstly, a review of the propellant sloshing models were investigated; however, the 3D spherical pendulum slosh model is merely presented here. Secondly, the mass expulsion torques effects were studied to estimate how they affect the attitude of ESMO. Finally, a consumption model was developed to estimate the total ESMO propellant waste. In that way, the inertial properties of ESMO are not constants, and their terms become time depending within the equations of motion. The primarily interest was focused on the internal dynamics since it was intended to analyse their effect on the ESMO motion in both its orbit and the attitude dynamics. In the model studied, these two dynamic equations are uncoupled; in fact, the environmental torques were not included in the dynamical system, which are usually the coupling terms in the equations of motion.

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