Many engineering applications involve the solution of optimal control problems. Such problems cover a wide variety of different disciplines, starting from typical aerospace applications, e.g. a fuel minimal launcher ascent trajectory, up to more exotic applications such as the optimal motion of the human body in different sport disciplines. This thesis presents a new method for solving a general class of multi-phase trajectory optimization problems. This new method uses a combination of direct multiple shooting and direct collocation. Depending on the specific demands of the problem to solve, a different kind of transcription method can be used for each phase. In addition, the method can be combined with the indirect method. Once the adjoint differential equations are available in addition to the dynamic system, one or more phases can be modeled as indirect phases. Since the transversality conditions that are usually required for solving the multi-point boundary value problem are contained in the Karush-Kuhn-Tucker conditions of the NLP-solver, they need not be formulated explicitly. The benefits of combining direct and indirect methods is demonstrated on an Ariane
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