為了解決衛星發射軌跡的最佳化問題，我首先推導出載具動態方程式，接著以變分法找出最佳化軌跡，並針對該軌跡設計出一符合需求之載具。本文遇到的困難在於使用變分法時需要找出拉格朗日乘子的初始條件，為了找出初始條件我使用shooting method 並配上誤差矩陣加快搜尋速度，在本文中誤差矩陣可在兩個和三個未知數的條件下加快搜尋初始條件的速度。 This paper investigated the optimal satellite launcher trajectories. We derived the equations of motion for the satellite launcher and solved the optimal problem with the method of Hamiltonian minimization. A launcher suited the requirements was proposed. The main difficulty of solving optimal problem with Hamiltonian Minimization is that we have to search for initial conditions. By using shooting method and Error Matrix, we can find initial conditions and save computing time. In the case of two or three unknown initial conditions, we successfully use Error Matrix to save computing time.
