Minimum time ascent phase trajectory optimization using steepest descent method

In this paper, ascent phase gravity turn trajectory of a launch vehicle is taken into account. Minimum-time problem of optimization is considered for specified structural and propulsive data. The objective is to achieve the target in minimum time and minimum error at terminal point by taking into account all the constraints. Trajectory generation is done for a single stage rocket in 2-D plane and computed for a given initial and final conditions. Hamiltonian is formulated by converting the given problem into secure final flight path angle problem and Pontryagin minimum principle is used to find the necessary conditions. The non-linear equations are solved using gradient method. Ultimately, the numerical results are evaluated and validity of result is exhibited.