عنوان مقاله [English]
The problem studied in this paper consists of the optimal launch of a satellite to a circular orbit of the earth. The effect of
the air resistance is also taken into consideration. The equations of optimal launch are first derived and the main problem is converted to a Two-Point Boundary Value Problem (TPBVP). A set of state and co-state variables, corresponding to the ideal case of planar earth with no air resistance, i.e. the case in which the linear tangent guidance law is, in fact, optimal, is used as an initial
guess, in order to solve the TPBVP using the shooting algorithm. A gradual or step-by-step introduction of the air resistance effect
is shown to make the numerical computations converge, thus, alleviating the problems caused by the shooting algorithm's sensitivity to the initial guess. Simulations reveal that the proposed method also has a satisfactory speed of convergence.