1. Problem formulation
This section formulates the hybrid optimal control problem for both trajectory and thrust profile. Optimality conditions are then expressed by applying the Pontryaguin Maximum Principle (PMP).
1.1 Optimum control problem
We're looking for the trajectory with minimum consumption for a launcher's last stage to reach an orbit from given initial conditions. The vehicle is considered as a material point, and the trajectory takes place outside the atmosphere. The dynamic equations in a geocentric inertial reference frame are as follows:
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Problem formulation
Analytical solution
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