Optimal mixed impulsive and continuous thrust trajectories to the interior Earth-Moon L₁ Lagrange point

Optimal transfer trajectories are designed for the spacecraft using mixed impulsive and continuous thrust propulsion to depart low-Earth orbit and enter a specified planar Lyapunov orbit at the interior Earth-moon Lagrange point in the framework of the planar circular restricted three body problem. The continuous dynamic optimization problem is reformulated as a discrete optimization through direct transcription and collocation, which then is solved using a nonlinear programming software. Then, the design parameters are specified as the flight time and the thrust weighting factor between impulsive thrust and continuous thrust in advance. Two different types of Earth departure trajectories are designed versus the thrust weighting factor using two separate performance indices. The numerical convergences of these transfer trajectory design methods are verified by producing the transfer trajectories versus varying numbers of nodes. Finally, low Earth orbit transfer trajectories using quadratic performance are designed and discussed by employing the progressive homotopy continuation method.