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Mathematical problems of orbital manoeuvres with single-input control

The role of small inexpensive satellites continuously grows in the modern space exploration. Their use can significantly reduce the cost of the mission. However the orbital control of such satellites is a challenge. One of the major issues here is that such satellites usually do not possess a complex attitude control system and three-axis stabilization might be unavailable. As a consequence, the thrust vector of the orbit control system cannot be arbitrary oriented in space and a rather involved mathematical methods are needed in order to compensate the control system simplicity.

The most frequently used simple and lightweight passive systems of one-axis stabilization are spin, passive magnetic or aerodynamic stabilization. In this case, one or two orbit control thrusters can be installed along the stabilized axis, so the orientation of the thrust vector at any given moment in time is determined by the orientation of stabilized axis. A very similar situation we face if the satellite uses the radiation pressure from the Sun as a motive force. Recently a serious progress was achieved in analysis and solution of respective control problems.

In this talk I plan to address the following problems: formation flying, deorbiting, transference from one orbit to another.

 
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