Optimization of the Ascent Trajectory of a 4-Stage Launching Vehicle for Geosynchronous Missions

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Optimization of the Ascent Trajectory of a 4-Stage Launching Vehicle for Geosynchronous Missions

W. Duffek

In connection with the geosynchronous mission of the German-French communication satellite Symphonie, the ascent trajectories of the Europa 2 vehicle, which was first developed for this mission, were studied. A nominal nearly geosynchronous primary orbit studied was used as target orbit. The investigated trajectory to this primary orbit consists of 5 thrust phases and 2 coast phases. The mathematical model for the vehicle considers all essential effects. The controls are determined such that the mass delivered in the primary orbit attains a maximum. This optimization problem was formulated as a boundary value problem with parameter optimization in an inner loop and was solved by the multiple shooting method. Initially optimal ascent trajectories for the nominal vehicle with fixed mass balance are given. The effect of a change in the staging ratio of the 4th stage on the increase of payload was investigated. The influence of given technical and operational constraints on the payoff function was determined. (Author)