An indirect method for optimizaing the three-dimensional ascent trajectory of a two-stage rocket leaving a rotating Earth is presented. The procedure assumes that the trajectory is divided into a succession of arcs by corners, i.e., points where discontinuities of the flight strategy occur. By replacing the time with a new independent variable, the corner positions are fixed: the boundary value problem is simplified and can be solved by means of an efficient procedure based on Newton's method. The optimization method is used in this paper to analyze the finite-thrust ascent to orbit, taking into account the maximum admissible value of the dynamic pressure, which is related to the thermal and mechanical loads that act on the rocket structure. The necessary conditions for optimizing the trajectory and obtaining the maximum payload are derived. Numerical results confirm the efficiency of the proposed method, even when the problem formulation introduces jumps in the state, adjoint and control variables.
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