Graduate Courses

5-Year Graduate Plan

Program Pre-requisites

Introduction to Aerospace Systems

Aerodynamics I

Aerodynamics II

Aero5 by Adrian HoodThe graduate faculty in Aerospace Engineering are continually developing and offering new special topic graduate courses. A listing of currently available graduate-level courses is provided below.

ENAE 601 Astrodynamics (3 credits)

Prerequisites: ENAE 404 and ENAE 441. Mathematics and applications of orbit theory, building upon the foundations developed in ENAE 404 and ENAE 441. Topics include two body orbits, solutions of Kepler's equation, the two-point boundary value problem, rendezvous techniques, and Encke's method.
Course Syllabus [pdf]

ENAE 602 Spacecraft Attitude Dynamics and Control (3 credits)

Prerequisites: ENAE 404 and ENAE 432. Rigid body rotational dynamics of spacecraft; forced and unforced motion, torques produced by the orbital environment; orbit/attitude coupling; gas jet, momentum wheel, and magnetic torque actuators. Elementary feedback attitude regulators and algorithms for linear and nonlinear attitude tracking.

ENAE 631 Helicopter Aerodynamics I (3 credits)

Prerequisites: ENAE 311 and ENAE 414 or permission of both department and instructor. A history of rotary-wing aircraft, introduction to hovering theory, hovering and axial flight performance, factors affecting hovering and vertical flight performance, autorotation in vertical descent, concepts of blade motion and control, aerodynamics of forward flight, forward flight performance, operational envelope, and introduction to rotor acoustics.

ENAE 632 Helicopter Aerodynamics II (3 credits)

Prerequisites: ENAE 631; and ENAE 311 and ENAE 414 or equivalent and permission of the department. Basic aerodynamic design issues associated with main rotors and tail rotors, discussion of detailed aerodynamic characteristics of rotor airfoils, modeling of rotor airfoil characteristics, review of classical methods of modeling unsteady aerodynamics, the problem of dynamic stall, review of methods of rotor analysis, physical description and modeling of rotor vortical wakes, discussion of aerodynamic interactional phenomena on rotorcraft, advanced rotor tip design, physics and modeling of rotor acoustics.

ENAE 633 Helicopter Dynamics (3 credits)

Prerequisite: ENAE 631 and permission of the department. Flap dynamics. Mathematical methods to solve rotor dynamics problems. Flap-lag-torsion dynamics and identify structural and inertial coupling terms. Overview on rotary wing unsteady aerodynamics. Basic theory of blade aeroelastic stability and ground and air resonance stability, vibration analyses and suppression.

ENAE 634 Helicopter Design (3 credits)

Prerequisite: ENAE 631 and permission of the department. Principles and practice of the preliminary design of helicopters and similar rotary wing aircrafts. Design trend studies, configuration selection and sizing methods, performance and handling qualities analyses, structural concepts, vibration reduction and noise. Required independent design project conforming to a standard helicopter request for proposal (RFP).

ENAE 635 Helicopter Stability and Control (3 credits)

Prerequisite: ENAE 631 and ENAE 642 or permission of department. Advanced dynamics as required to model rotorcraft for flight dynamic studies. Development of helicopter simulation models and specifications of handling qualities. Methods for calculation of trim, poles, frequency response, and free flight response to pilot inputs.

ENAE 640 Atmospheric Flight Mechanics (3 credits)

Prerequisite: ENAE 403 or permission of department. Studies in the dynamics and control of flight vehicles. Fundamentals of the dynamics of rigid and non-rigid bodies and their motion under the influence of aerodynamic and gravitational forces.

ENAE 641 Linear System Dynamics (3 credits)

Prerequisite: ENAE 432. Linear systems; state space, multi-input, multi-output models; eigenstructure; controllability, observability, singular value analysis; multivariable Nyquist condition; observer design; introduction to Kalman filtering. Full state feedback techniques including pole placement and LQR/LQG techniques; introduction to loop shaping and robustness.

ENAE 642 Atmospheric Flight Control (3 credits)

Prerequisites: ENAE 432 and ENAE 403, or equivalents. Exposure to flight guidance and control. Draws heavily from vehicle dynamics as well as feedback theory, and careful treatment of the non-linear aspects of the problem is critical. Conventional sythesis techniques are stressed, although modern methods are not ignored. Multivariable system analysis is included, along with flight-control design objectives and hardware limitations. Emphasis on aircraft and missiles. Course Syllabus [pdf]

ENAE 646 Advanced Dynamics of Aerospace Systems (3 credits)

Prerequisite: ENAE301 (Formerly: ENAE788G. Credit only granted for: ENAE788G or ENAE646) Introduces the principles and methods for formulating and analyzing mathematical models of aerospace systems using Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid body dynamics. Additional topics include applied dynamical systems, geometric mechanics, and symmetry and reduction.  Course Syllabus [pdf]

ENAE 647 Flexible Multi-body Dynamics (3 credits)

Prerequisite: ENAE646. (Formerly: ENAE788Q. Credit only granted for: ENAE788Q or ENAE647). Review of Particle Dynamics, kinematics of rigid motion, kinematics and kinetics of rigid bodies, analytical dynamics, constraint equations in multibody dynamics, methods for enforcing kinematic constraints, formulation of flexible bodies in multibody dynamics, finite element modeling, and numerical integration methods. Course Syllabus [pdf]

ENAE 651 Smart Structures (3 credits)

Topics related to the analysis, design, and implementation of smart structures and systems: modeling of beams and plates with induced strain actuation; shape memory alloys; electro-rheological fluids; magnetostrictor and electrostricter actuators and fiber optic sensors.

ENAE 652 Computational Structural Mechanics (3 credits)

Prerequisite: permission of the department. Fundamentals of structural mechanics and computational modeling. Finite element modeling of two- and three-dimensional solids, plates and shells. Geometrically nonlinear behavior. Structural stability such as buckling and postbuckling.

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ENAE 653 Nonlinear Finite Element Analysis of Continua (3 credits)

Prerequisite: ENAE 652 or equivalent. Finite element formulation of nonlinear and time dependent processes. Introduction to tensors, nonlinear elasticity, plasticity and creep. Application to nonlinear solids including aerospace structures, such as shells undergoing finite rotations.

ENAE 654 Mechanics of Composite Structures (3 credits)

Prerequisite: ENAE 452 or permission of both department and instructor.. Corequisite: ENAE 423 or equivalent. An introduction to structures composed of composite materials and their applications in aerospace. In particular, filamentary composite materials are studied. Material types and fabrication techniques, material properties, micromechanics, anisotropic elasticity, introduction to failure concepts.

ENAE 655 Structural Dynamics (3 credits)

Prerequisite: ENAE 452 or permission of department. Advanced principles of dynamics necessary for structural analysis; solutions of eigenvalue problems for discrete and continuous elastic systems, solutions to forced response boundary value problems by direct, modal, and transform methods.

ENAE 656 Aeroelasticity (3 credits)

Prerequisite: ENAE 655 or permission of department. Topics in aeroelasticity: wing divergence; aileron reversal; flexibility effects on aircraft stability derivatives; wing, empennage and aircraft flutter; panel flutter; aircraft gust response; and aeroservoelasticity of airplanes.

ENAE 663 Introduction to Plasmas for Space Propulsion and Power (3 credits)

Prerequisite: PHYS411 and permission of instructor. Credit will be granted for only one of the following: ENAE788L or ENAE663. Formerly ENAE788L. Characteristics of plasmas, motion of charged particles in fields, collisional processes, kinetic theory, fluid description of plasmas, transport properties, equilibrium vs. non-equilibrium, generation of plasmas.
Course Syllabus [pdf]

ENAE 665 Advanced Airbreathing Propulsion (3 credits)

Prerequisite: ENAE455 and ENAE674 or equivalent; and permission of instructor. Advanced treatment of airbreathing propulsion technologies, propulsion system analysis, and engine/airframe integration. Topics will vary, but may include novel engine cycles, advanced gas turbine systems, pulsed systems, and high-speed engines, including scramjets and combined cycle systems.

ENAE 667 Advanced Space Propulsion and Power (3 credits)

Prerequisite: ENAE788L and permission of instructor. Advanced treatment of selected space propulsion and power technologies, methods of analysis and performance estimation. Topics will vary each year as time permits, but may include cold gas systems, chemical, nuclear, arcjets, beamed energy, and electric propulsion systems, as well as other advanced concepts.
Course Syllabus [pdf]

ENAE 670 Fundamentals of Aerodynamics (3 credits)

Prerequisite: permission of department. Introduction to aerodynamics for aerospace engineering students specializing in fields other than aerodynamics. Broad coverage of flight regimes, inviscid theory, incompressible theory, subsonic compressible flow, linearized supersonic flow, hypersonic flow, viscous flows, Navier-Stokes equations, boundary layer theories.

ENAE 672 Low Reynolds Number Aerodynamics (3 credits)

Prerequisite: ENAE414 and permission of instructor. Survey and review of incompressible flow concepts including potential flow, lift and drag, and the Navier-Stokes equations with a focus on low Reynolds number applications. Boundary layers, separation, and transition. Viscous flows. Vortex-dominated flows and vortex dynamics. Introduction to unsteady and three-dimensional aerodynamics such as dynamic stall, Wagner effect, and flapping wings.
Course Syllabus [pdf]

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ENAE 674 Aerodynamics of Compressible Fluids (3 credits)

Prerequisite: ENAE 311 and ENAE 414; or ENME 331 or ENME 640 or equivalent; or permission of department.
One-dimensional flow of a perfect compressible fluid. Shock waves. Two-dimensional linearized theory of compressible flow. Two-dimensional transonic and hypersonic flows. Exact solutions of two-dimensional isotropic flow. Linearized theory of three-dimensional potential flow. Exact solution of axially symmetrical potential flow. One-dimensional flow with friction and heat addition.
Course Syllabus [pdf]

ENAE 676 Turbulence (3 credits)

Prerequisite: ENAE672. Recommended: ENAE674.
Physical and statistical descriptions of turbulence; review of phenomenological theories for turbulent flows; scales of motion; correlations and spectra; homogeneous turbulent flows; inhomogeneous shear flows; turbulent flows in pipes and channels; turbulent boundary layers; theory of methods for turbulent flows (Reynolds stress equations, LES, DES, DNS); experimental methods for turbulence measurements.

ENAE 681 Engineering Optimization (3 credits)

Prerequisite: permission of department. Methods for unconstrained and constrained minimization of functions of several variables. Sensitivity analysis for systems of algebraic equations, eigenvalue problems, and systems of ordinary differential equations. Methods for transformation of an optimization problem into a sequence of approximate problems. Optimum design sensitivity analysis.

ENAE 682 Hypersonic Aerodynamics (3 credits)

Prerequisite: permission of department. Hypersonic shock and expansion waves, Newtonian theory, Mach methods, numerical solutions to hypersonic inviscid flows, hypersonic boundary layer theory, viscous interactions, numerical solutions to hypersonic viscous flows. Applications to hypersonic vehicles.
Course Syllabus [pdf]

ENAE 683 High Temperature Gas Dynamics (3 credits)

Prerequisite: permission of department. Aspects of physical chemistry and statistical thermodynamics necessary for the analysis of high temperature flows, equilibrium and nonequilibrium chemically reacting flows, shock waves, nozzle flows, viscous chemically reacting flow, blunt body flows, chemically reacting boundary layers, elements of radiative gas dynamics and applications to hypersonic vehicles.
Course Syllabus [pdf]

ENAE 684 Computational Fluid Dynamics I (3 credits)

Prerequisite: permission of department. Partial differential equations applied to flow modelling, fundamental numerical techniques for the solution of these equations, elliptic, parabolic, and hyperbolic equations, elements of finite difference solutions, explicit and implicit techniques. Applications to fundamental flow problems.
Course Syllabus [pdf]

ENAE 685 Computational Fluid Dynamics II (3 credits)

Prerequisite: ENAE 684 or permission of department.
Continuation of ENAE 684. Basic algorithms for the numerical solution of two and three dimensional inviscid and viscous flows. Applications to internal and external flow problems.
Course Syllabus [pdf]

ENAE 688 Seminar (1-3 credits)


ENAE 691 Satellite Design (3 credits)

Prerequisite: ENAE 483. Systems design of Earth-orbiting satellites, including geostationary communications satellites and low Earth orbit constellations. Basics of orbital motion, communications, and instrument design. Spacecraft systems, structural design, thermal design, power generation, and attitude determination and control. Launch vehicle interfacing and mission operations.

ENAE 692 Introduction to Space Robotics (3 credits)

Analysis techniques for manipulator kinematics and dynamics. DH parameters, serial and parallel manipulators, approaches to redundancy. Applications of robots to space operations, including manipulators on free-flying bases, satellite servicing, and planetary surface mobility. Sensors, actuators, and mechanism design. Command and control with humans in the loop.
Course Syllabus [pdf]

ENAE 693 Space Simulation (3 credits)

Physical characteristics of the space environment, and approaches to simulating them on Earth. Systems modeling; kinematics and dynamics. Required degrees of freedom and levels of fidelity. Physical simulations, including neutral buoyancy, air-bearing, and motion carriages. Instrumentation and data collection, error analysis, correlation, and performance metrics.

ENAE 694 Spacecraft Communications (3 credits)

Brief overview of satellite orbits. Radio frequency communications, noise, and bandwidth limitations. Link budget analysis. Modulation and multiplexing approaches, multiple access systems. Satellite transponder and Earth station technology.

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ENAE 696 Spacecraft Thermal Design (3 credits)

Thermal sources in space. Black-body radiation; absorptivity and emissivity; radiative thermal equilibrium. Mutually radiating plates, view angles, and interior conduction. Techniques of spacecraft thermal analysis; approaches to passive and active thermal control.

ENAE 697 Space Human Factors and Life Support (3 credits)

Engineering requirements supporting humans in space. Life support design: radiation effects and mitigation strategies; requirements for atmosphere; water, food, and temperature control. Accommodations for human productivity in space: physical and psychological requirements; work station design; and safety implication of system architectures. Design and operations for extra-vehicular activity.

ENAE 741 Interplanetary Navigation and Guidance (3 credits)

Prerequisites: ENAE432 and ENAE601. Interplanetary trajectory construction; patched and multiconic techniques. Methods of orbit and attitude determination; applied Kalman filtering. Guidance algorithms and B-plane targeting. Interplanetary navigation utilizing in situ and radio techniques.
Course Syllabus [pdf]

ENAE 742 Robust Multivariable Control (3 credits)

Limitations on achievable performance in multivariable feedback systems due to uncertainty. Singular values, matrix norms, multivariable Nyquist stability theory, uncertainty modeling in aerospace systems. Loop-shaping, generalization of Bode design principles. Characterizing the uncertainty, robustness and performance analysis, and synthesis, primarily in the frequency domain. Current research directions. Aerospace examples are used to complement the theory.

ENAE 743 Applied Nonlinear Control of Aerospace Vehicles (3 credits)

Prerequisite: ENAE641. Modern methods of analysis and synthesis of multivariable nonlinear control techniques for aircraft, spacecraft, and space manipulator systems. Topics include passivity and Lyapunov theory, feedback linearization, nonlinear observers, Hamiltonian methods, robust controller design, and an introduction to adaptive nonlinear control methods. Course Syllabus [pdf]

ENAE 757 Advanced Structural Dynamics (3 credits)

Prerequisite: ENAE655 or equivalent. Model correlation and updating of multi degree-of-freedom structural systems. Wave propagation analysis of structural dynamics. Structural health monitoring and damage detection methods. Stationary and non-stationary methods for vibration analysis. Applications include rotorcraft, aircraft, and spacecraft structures.

ENAE 788 Selected Topics in Aerospace Engineering (1-3 credits)  

ENAE788A: Fundamentals of Explosions: Natural, Accidental, and Controlled (3 credits)

Introduces the physics and chemistry of explosions and investigates how they occur naturally, accidentally, and by engineering design.
Course Syllabus [pdf]

ENAE 788G Advanced Dynamics (3 credits)

Prerequisite: ENAE301, ENAE788Q or equivalent.
This course introduces the principles and methods for formulating and analyzing mathematical models of aerospace systems using Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid body dynamics. Additional topics include applied dynamical systems, geometric mechanics, and symmetry and reduction.

ENAE 788N Near-Earth Object Exploration

This course provides an overview of the near-Earth objects (NEOs) of our solar system|the asteroids and comets whose orbits closely approach Earth's orbit|and what we know about them, what we're learning about them, and how to design spacecraft missions to interact with them.
Course Syllabus [pdf]

ENAE 791 Launch and Entry Vehicle Design (3 credits)

Prerequisite: ENAE 601. Design of aerospace vehicles for atmospheric transit to and from space. Generic formulation of atmospheric flight dynamics. Ballistic and lifting entry trajectories. Estimation of vehicle aerodynamic properties and aerothermodynamic heating. Entry thermal protection design. Trajectory analysis of sounding rockets and orbital launch vehicles. Serial, parallel, and hybrid multistaging schemes, optimal multistaging. Constrained trajectory optimization. Launch vehicle economic and reliability analysis, flight termination systems, sensors and actuators.

ENAE 799 Master's Thesis Research (1-6 credits)


ENAE 898 Pre-Candidacy Research (1-8 credits)


ENAE 899 Doctoral Dissertation Research (1-8 credits)

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