The optimization of launch trajectory of low-altitude satellites for minimum-fuel consumption is investigated. A two-stage solid-propellant rocket launcher is considered for this study. The second-stage trajectory is optimized by using the optimal control theory based on the variation of caculus. Three numerical methods, shooting method, quasi-linearization method and gradient method, are developed for solving this problem. For the first-stage flight, the same approach is not feasible because of aerodynamic and structural constraints unless these constraints are imbedded into the optimization problem. In this study, a parametric study is conducted for the first-stage flight to find the admittable set of the launch trajectories. Combining the first-stage and second-stage flights, the minimum-fuel launch trajectory is found.
