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Optimization in Aerospace Engineering


Credit Hours:


Learning Objective:

To introduce students to the theory and numerical calculation of optimal space trajectories. This course provides the essential technical components of space trajectory design and space trajectory optimization. Students develop basic engineering skills in formulating and solving open-ended problems and in writing a project report. Some students have turned their projects into directed studies (AAE 590), conference papers, and journal submissions.


Formulation of optimization problems encountered in aerospace engineering. Minima of functions and functionals, necessary conditions, calculus of variations, control formulation, two-point boundary-value problems. Applications to typical problems in aerospace engineering such as optimal launch, minimum time to climb, maximum range, and optimal space trajectories. Fall 2015 Syllabus

Topics Covered:

The Problems of Bolza, Lagrange and Mayer; Interchangeability of the problems, introductory concepts, Zermelo's problem, Lotka-Volterra model; Proof of the Euler-Lagrange Theorem; Calculus of variations, necessary conditions, transversality conditions, TPBVP; Example of flat Earth launch problem and derivation of linear and bilinear tangent steering laws; Proof of the Weierstrass Necessary Condition;Statement of the Maximum Principle; Flight envelopes for subsonic and super-sonic aircraft, minimization of time to climb, maximization of the range of a rocket, optimal launching of a satellite; Proof of the Weierstrass???Erdmann Corner Conditions;Optimal Control Problems with Inequality Constraints;Bounded control problem, singular subarcs, switching functions, generalized Legendre-Clebsch condition;General Theory of Optimal Rocket Trajectories;Extremal arcs, impulsive, thrust, optimal trajectories in a uniform field, the primer in a inverse square field, orbital transfer maneuvers; Computational techniques; Trajectory design, trajectory optimization.


Students should be senior or graduate standing in engineering, science, or mathematics.

Applied / Theory:

30 / 70

Web Address:

Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions and quizzes.


Once a week assignments accepted via Internet.


Yes. Students select individual projects on optimization in aerospace engineering. Written proposals, progress reports, and a final report are required.


Three exams. No final exam.


Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Required - Longuski, J.M., Guzman, J. J., and Prussing, J.E., Optimal Control with Aerospace Applications, Springer, New York, 2014; ISBN: 978-1461489443.

Computer Requirements:

ProEd Minimum Computer Requirements. Trajectory design and optimization software will be made available to students for homework assignments and for the projects.

ProEd Minimum Requirements: