Graduate Courses
The 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
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. (Sample Course Syllabus)
ENAE 602 Spacecraft Attitude Dynamics and Control
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
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
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
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
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
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 641 Linear System Dynamics
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
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.
ENAE 644 Optimal Control of Aerospace Systems
Prerequisites: ENAE 432, ENAE 403 or ENAE 404, or equivalents. Formal optimization of linear and non-linear dynamic systems, developed rigorously via the calculus of variations - first and second variations. Treatment of dynamic constraints, terminal conditions, fixed and free final times. Numerical techniques to the non-linear optimization problem are stressed. Investigation of optimal aerodynamic shapes, trajectory optimization, optimal flight guidance. Final project includes numerical analysis.
ENAE 651 Smart Structures
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
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.
ENAE 653 Nonlinear Finite Element Analysis of Continua
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
Prerequisite: permission of both department and/or 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
Prerequisite: ENAE 423 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
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 661 Advanced Propulsion I
Prerequisites: ENAE 455; and ENAE 457. Special problems of thermodynamics and dynamics of aircraft power plants; jet, rocket and ramjet engines. Plasma, ion and nuclear propulsion for space vehicles.
ENAE 662 Advanced Propulsion II
Prerequisites: ENAE 455; and ENAE 457. Special problems of thermodynamics and dynamics of aircraft power plants; jet, rocket and ramjet engines. Plasma, ion and nuclear propulsion for space vehicles.
ENAE 670 Fundamentals of Aerodynamics
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 674 Aerodynamics of Compressible Fluids
Prerequisite: ENAE 471 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. (Sample Course Syllabus )
ENAE 681 Engineering Optimization
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
Prerequisite: permission of instructor. 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.
ENAE 683 High Temperature Gas Dynamics
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. (Sample Course Syllabus)
ENAE 684 Computational Fluid Dynamics I
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. ( Sample Course Syllabus )
ENAE 685 Computational Fluid Dynamics II
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. (Sample Course Syllabus )
ENAE 691 Satelite Design
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
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. (Sample Course Syllabus)
ENAE 694 Spacecraft Communications
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.
ENAE 696 Spacecraft Thermal Design
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
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
Prerequisites: ENAE 432 and ENAE 601. 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.
ENAE 742 Robust Multivariable Control
Prerequisites: ENAE 432 or equivalent, plus graduate-level exposure to linear systems and linear algebra. 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
Prerequisite: ENAE 641. 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.( Sample Syllabus )
ENAE 757 Advanced Structural Dynamics
Prerequisite: ENAE655 or equivalent; ENAE644 or equivalent; ENAE651 or equivalent
This course will demonstrate the practical application of Smart Materials and Spatially Distributed Transducers to the design and control of advanced structures. The course will be focused toward the active control of continuum structures using advance Spatially Distributed Parameter System control techniques and concepts. Effective system parameterizations will be used to reduce distributed parameter system models to classical canonical state space form for the purpose of robust adaptive structure design. Application case studies, including morphing structures will be employed as necessary to enhance the students intuition and understanding of Distributed Parameter Systems.
ENAE 788 Selected Topics in Aerospace Engineering 1-3 credits
ENAE 788C Microsystem Flight Dynamics and Control
Prerequisites: ENAE 641, or equivalent; ENAE 403 or equivalent
An in-depth analysis of the major topics related to insect flight, including dynamics, biomechanics, unsteady aerodynamics, visual processing, mechanoreception, sensory feedback. Application of biologically inspired multivariable control and estimation techniques to aerial microsystems, including rotary and flapping wing vehicles. Translation of performance and handling quality specifications into control system designs, and discussion of sensing and actuation technologies with an emphasis on size, weight, and power constraints.
ENAE 788D Advanced Space Systems Design, Dr. Akin
ENAE 788G Advanced Dynamics of Aerospace Systems, Dr. Paley
Prerequisite: ENAE301 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 788K Control of Stochastic Systems, Dr. Sanner
ENAE788L Introduction to Plasmas for Space Propulsion
Prerequisites: PHYS 411 or equivalent, permission of instructor
This course will introduce the concepts, characteristics and analysis techniques for plasmas, with examples drawn from their application to space propulsion. Topics will include: Characteristics of plasmas, Motion of charged particles in fields, Collisional processes, Kinetic theory, Fluid description of plasmas, Transport
properties, Non-equilibrium and Creation of plasmas.
ENAE 788O Emerging Challenges in Aerospace, Dr. Hubbard
In this course we will engage in an immersive study of the feasibility of flight in the thin atmosphere of Mars with application to the exploration of extreme Martian environments (e.g., canyons, lava tubes). With an emphasis on systems analysis, students will examine cutting edge concepts and define potential solutions to achieve the mission objectives. Topics will include: Mars atmosphere and wind environment, energy generation on Mars (including airborne wind energy harvesting), aerial platform concepts (fixed wing, rotary wing, lighter than air, biologically inspired), and systems analysis techniques & tools. Guest lecturers and case studies also will be used to keep the discussions focused and well grounded. A final term project will be assigned that addresses the following areas:
- Science Goals/Mission Scenarios
- Data Mining from Technical Experts on the Martian Environment and Relevant Technologies
- Mission Requirements
- Vehicle Requirements
- Vehicles Configurations
- Initial Assessment of Vehicle Configurations
- Detailed System Analysis of Selected Vehicle Configuration
ENAE 788U Planetary Surface Robotics, Dr. Akin
ENAE 788W Smart Fluids & Applications, Dr. Wereley
ENAE 788Y Advanced Control for Robotics, Dr. Akin
ENAE 791 Launch and Entry Vehicle Design
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
ENAE898 Pre-Candidacy Research 1-8 credits
ENAE 899 Doctoral Dissertation Research 1-8 credits
