A common approach to solving infinite dimensional optimal control problems, such as in launch vehicle trajectory optimization, is to approximate the optimal control function as a set of parameters. This process, known as the direct method, transcribes the optimal control problem into a finite dimensional parameter optimization problem. Traditionally, subject matter experts and trajectory analysts work manually to find usable trajectories by changing the initial guess for the control parameters. This paper presents a method to capture the feasible design space of a launch vehicle trajectory problem. The result is a region of feasible values for the launch vehicle control parameters. In this context, feasibility is denned by the trajectory reaching the termination criteria, thereby returning a function evaluation. The method is applied to a Delta IV Medium launch vehicle. This vehicle is used because it represents the challenges of trajectory optimization for ETO launch vehicles while not being overly complex. Two ways of sampling the control parameter design space to determine feasibility are compared. Results are represented using design variable limits and the global feasible space is shown directly using scatter-plot matrices.
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