Same as AE4881. This course covers the theory, computation and practical implementation of integrated trajectory planning and guidance algorithms for aerospace vehicles. The theory is based on the next generation of dynamical systems in mechanical and aerospace engineering. Examples will be drawn from a sample of DoD problems in space systems, missile engineering and small munitions. After a review of the state of practice, a unified theoretical framework for solving practically constrained trajectory problems will be developed. The Karush-Kuhn-Tucker conditions will form the foundations of constraint violation and validating optimality conditions. Multiplier theory and its use in solving practical problems will be covered from a real-time computational viewpoint. No-fly zones and engineering requirements will be formulated as a mathematical mixture of state and decision-variable constraints. Extensive MATLAB-based mini-projects will form the core of the laboratory experience. These projects are designed for students to learn the process of constructing a flyable trajectory planning algorithm from first principles to an integrated guidance system.