Minimum-fuel lunar transfers with engine switching and transients
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The investigation of minimum-fuel planar Lunar transfers are investigated for a variety of mission profiles. The problem is set within the context of the classic restricted three-body problem. Two different types of propulsive systems are studied including electric propulsion and nuclear thermal rockets (NTR) providing a range of initial thrust-to-weight ratios. The solution of the transfers is achieved by solving a series of simpler subproblems to obtain an estimate of the fully optimal trajectory. The series of subproblems is solved by a new dynamic boundary evaluation method. The full solution is then found using this estimate and a hybrid "direct/indirect" method. This solution determines the total time-of-flight based on a fixed thrust-coast-thrust engine firing sequence. The optimal transfers for a range of initial thrust-to-weight ratios are found and presented. The true optimal solution for a power limited spacecraft for a fixed time-of-flight depends on the engine firing switching function. The solution of the switching problem is extremely difficult and a three-stage methodology is developed. The first stage uses mixed-integer nonlinear programming (MINLP) to approximate the switching function's discrete characteristics. The second stage uses the MINLP solution and problem characteristics to solve a relaxation of the full switching problem and the final stage solves the full two-point boundary value problem from the estimates of the preceding stages. The switching solutions for a range of flight times are presented. The use of NTR propulsion introduces thrust transients which are modeled using the point mass mono-energetic nuclear equations and the rocket itself is modeled by a lumped heat-exchange system. The effects on an optimal transfer of the transients is found and presented.