Aerospace engineering

Introduction to the optimization of aerospace vehicle trajectories. Non Linear Programming: problem definition; existence of a minimum; the unconstrained problem; the problem with inequality and equality constraints. Calculus of Variations: overview of variational problems; the method of Lagrange multipliers; free variational problems; Euler-Lagrange equations; special cases of the Euler-Lagrange equation; the case of derivatives of order higher than the first; variational problems with variable extrema; transversality conditions; the case of multiple unknown functions; problems with integral (isoperimetric) constraints; Isoperimetric problems with multiple unknown functions and multiple integral constraints. Optimal control problems. General description of the problem and application to the case of optimization of aerospace trajectories: minimum transfer time problems; problems with minimum mass consumption of propellant; boundary and isoperimetric constraints of the trajectories; Euler-Lagrange equations; conditions of transversality. The Pontryagin problem: formulation of the trajectory optimization problem; thrust optimality and “primer vector”. Comparison with optimal control problems. Development of mathematical models and their numerical implementation for performance optimization. Cases studied: • Optimizing the performance of an airplane. • Ascent trajectory of a launcher and entry into Earth orbit; • Trajectory for an orbital transfer (planetary/interplanetary); • Lunar soft-landing;

basic knowledge of flight mechanics

lecture notes and copies of book chapters

classroom lessons

evaluation of the numerical exercises proposed during the course and oral questions on the program

Oral exam in presence