Aerospace Engineering
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Graduate Courses
The faculty has approval to offer the following courses in the academic years 20012002 and 20022003; however, not all courses are taught on a regular basis. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.
Unless otherwise stated below, each course meets for three lecture hours a week for one semester.
380P. Mathematical Analysis for Aerospace Engineers.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Analytical Methods I.
Introduction to modern mathematics, real analysis of functions of one variable, linear algebra, elements of real analysis of functions of many variables, calculus of variations.
Topic 2: Analytical Methods II.
Elements of complex analysis, Fourier and Laplace transforms, ordinary and partial differential equations, perturbation methods.
Topic 4: Numerical Methods in Ordinary Differential Equations.
Onestep, multistep, and extrapolation methods for solving stiff and nonstiff equations; discretization errors and stability; computer solution of selected problems.
381P. System Theory.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Linear Systems Analysis.
Linear dynamical systems; controllability and observability; Liapunov stability; realization theory; statefeedback and observers; leastsquares optimization; elements of linearquadratic optimal control.
Topic 2: Multivariable Control Systems.
Multivariable feedback systems; factorizations and controller parameterization; limitations and tradeoffs of feedback; robust stability and performance; robust control design; computeraided design methodologies. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.
Topic 3: Optimal Control Theory.
Necessary conditions and sufficient conditions for the parameter optimization and optimal control problems; engineering applications.
Topic 4: Numerical Methods in Optimization.
Numerical methods for solving parameter optimization, suboptimal control, and optimal control problems.
Topic 6: Statistical Estimation Theory.
Least squares; sequential and batch processors; optimal, linear, recursive, maximum likelihood, and minimum variance estimates; squareroot filtering; filter divergence; discrete and continuous Kalman filters.
Topic 7: Advanced Topics in Estimation Theory.
Estimation in the presence of unmodeled accelerations; nonlinear estimators; continuous estimation methods. Additional prerequisite: Aerospace Engineering 381P (Topic 6).
Topic 8: Stochastic Estimation and Control.
Linear and nonlinear estimation theory. Kalman filters, linear quadratic Gaussian (LQG) problem. Emphasis on applications. Additional prerequisite: Electrical Engineering 351K or the equivalent.
382Q. Fluid Mechanics.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Foundations of Fluid Mechanics.
Fundamental equations; constitutive equations for Newtonian fluids; inviscid, incompressible potential flow; viscous flow including exact solutions and boundary layer theory; compressible flow.
Topic 5: Boundary Layer Flows.
NavierStokes equations and the boundary layer approximation; effects of pressure gradients, compressibility, and heat transfer; emphasis on turbulent flows.
Topic 6: Finite Difference Methods in Computational Fluid Dynamics.
Mathematical formulation of the problems; finite difference representation of the derivatives; explicit formulations; implicit formulations; alternatingdirection implicit; KellerBox methods; linearization of equations.
Topic 7: Advanced Problems in Compressible Flow.
Physics and modeling of compressible fluids; types and structure of shock waves; heat conduction and secondary viscosity effects; exact nonlinear flow models.
Topic 8: Lagrangian Methods in Computational Fluid Dynamics.
Particlebased methods of computational fluid dynamics: molecular dynamics, direct simulation Monte Carlo, cellular automata, lattice Boltzmann, particle in cell, point vortex, immersed boundary.
382R. Aerodynamics.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 3: Hypersonic Aerodynamics.
Characteristics and assumptions of hypersonic flow; hypersonic similitude; Newtonian theory; constant density solutions.
Topic 4: Theoretical Gas Dynamics.
Linear and nonlinear models of steady and unsteady potential and rotational twodimensional and threedimensional flows of a perfect gas.
Topic 5: Advanced Computational Methods.
Development and implementation of numerical methods for solution of transport equations; computational grid generation; applications to fluid flows, including shock waves.
Topic 6: Molecular Gas Dynamics.
Same as Mechanical Engineering 381Q (Topic 4: Molecular Processes). Kinetic theory, thermodynamics, statistical mechanics. Applications: equilibrium gas properties, chemical kinetics, interaction of matter with radiation, rarefied gas dynamics. Additional prerequisite: Mechanical Engineering 326 or the equivalent.
Topic 7: Optical Diagnostics for Gas Flows.
Fundamentals of nonintrusive flowfield diagnostics for aerodynamics and combustion. Basics of lasers and optical detectors; interferometric methods; Rayleigh, Raman, and Mie scattering; absorption spectroscopy; laserinduced fluorescence.
384P. Structural and Solid Mechanics.
Three lecture hours or two lecture hours and three laboratory hours a week for one semester, depending on the topic. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Solid Mechanics I.
Same as Engineering Mechanics 388. Mathematical description of stress, deformation, and constitutive equations of solid mechanics; boundary value problems of elasticity.
Topic 2: Solid Mechanics II.
Same as Engineering Mechanics 388L. Additional topics in elasticity. Additional prerequisite: Aerospace Engineering 384P (Topic 1).
Topic 3: Structural Dynamics.
Same as Engineering Mechanics 384L. Free and forced vibration of singledegreeoffreedom, multipledegreeoffreedom, and continuous systems. Lagrange's equations and Hamilton's principle; discretization of continuous systems; numerical methods for response and algebraic eigenvalue problems.
Topic 4: Finite Element Methods.
Same as Computational and Applied Mathematics 394F and Engineering Mechanics 394F. Derivation and implementation of the finite element method; basic coding techniques; application to problems of stress and diffusion.
Topic 6: Advanced Structural Dynamics.
Analysis of complex flexible systems; discretization of complex structures by the finite element method; advanced computational methods for large finite element models. Additional prerequisite: Aerospace Engineering 384P (Topic 3) or Engineering Mechanics 384L.
Topic 7: Reliability Engineering.
Introduction to reliability engineering: basic concepts from statistics, the quantification of reliability and its related functions, analysis of reliability data, loadstrength, interference, reliability in design and testing.
Topic 8: Selected Topics in Aeroelasticity.
Classical and contemporary topics in aeroelasticity; general introduction to aeroelastic phenomena, including flutter, divergence, control reversal, and flexibility effects on stability and control; aeroelastic tailoring; active control concepts; unsteady aerodynamic theories for lifting surfaces and bodies; aeroelastic system identification, including nonlinear systems (theory and laboratory applications).
Topic 9: Structural Optimization.
New concepts in structural design, with emphasis on parameter optimization and algorithmic tools that have been found useful in structural analysis.
Topic 11: Mechanics of Composite Materials.
Constitutive equations; micromechanical and macromechanical behavior of lamina; strength and stiffness in tension and compression, theory of laminated plates; strength of laminates; delamination.
Topic 12: Experimental Methods in Structural Dynamics.
Timeseries analysis; timedomain and frequencydomain techniques of structural identification; exciters and sensors. Two lecture hours and three laboratory hours a week for one semester. Additional prerequisite: Aerospace Engineering 384P (Topic 3) or Engineering Mechanics 384L.
387P. Flight Mechanics, Guidance, Navigation, and Control.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Atmospheric Flight Mechanics.
General equations of motion for flight in resisting medium; trajectory analysis; aerodynamic stability and control.
Topic 2: Mission Analysis and Design.
Mission design and mission constraints, launch windows; rendezvous analysis; orbital design interactions with thermal and structural analysis; design of a typical mission.
Topic 3: Inertial Guidance and Navigation.
Review of rigid body dynamics; gyroscopic motion; accelerometers, applications to inertial guidance, error analysis; attitude control.
388P. Celestial Mechanics.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Hamiltonian Mechanics.
Hamiltonian equations of motion; canonical transformation; HamiltonJacobi equation; stability; small oscillations; first integrals and integral invariants; Lie series, canonical perturbation methods; von Zeipel and Hori methods. Additional prerequisite: Engineering Mechanics 381.
Topic 2: Celestial Mechanics I.
Series expansions applicable to the motion of two bodies; deterministic orbit determination; variational equations; introduction to the nbody and restricted problems.
Topic 3: Celestial Mechanics II.
Variation of parameters; special and general perturbations; potential of a nonspherical body; introduction to satellite theory; precession and nutation; astronomical constants and time. Additional prerequisite: Aerospace Engineering 388P (Topic 2).
Topic 4: Satellite Theory.
Potential of a solid body; canonical variables; averaging methods; canonical perturbation methods; resonance cases; thirdbody nongravitational effects; theories of motion of artificial and natural satellites. Additional prerequisite: Aerospace Engineering 388P (Topic 1) and 388P (Topic 3).
Topic 5: Theory of Orbits I.
Equations of motion of the restricted problem of three bodies; Jacobian integral; applications to earthtomoon and interplanetary trajectories; Hill's curves and surfaces of zero velocity, with applications to stability.
389P. Satellite Applications.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Determination of Time.
Concepts of time; fundamental reference system; polar motion; practical methods in time determination and dissemination; historical and presentday time scales; atomic clocks; time transfer via satellite.
Topic 2: Satellite Geodesy.
Representations of planetary gravitational fields; determination of spherical harmonic coefficients; geoids and gravity anomalies; temporal variations in the geopotential; planetary rotational dynamics.
Topic 3: Advanced Topics in Satellite Geodesy.
Solid earth and ocean tide models, tidal forces on satellites, surface displacements; nongravitational forces; frames of reference; and geodetic instrumentation. Additional prerequisite: Aerospace Engineering 389P (Topic 2).
Topic 4: Remote Sensing.
Introduction to fundamentals of active and passive electromagnetic radiation and associated satellite instruments, radiative transfer, and scattering theory; inference of geophysical parameters from remote sensing data. Term project work with satellite microwave, visual, and infrared data.
Topic 5: Remote Sensing Applications.
Theory and application to geodetic, oceanographic, and atmospheric problems of data from satellite sensors, including altimeters, radiometers, scatterometers, and synthetic aperture radars. Introduction to and use of national remotely sensed databases. Course content may vary.
Topic 6: Satellite Tracking Systems.
Review of frequency and time standards, frequency measurement; theory and application of electromagnetic radiation, propagation, and medium effects. Introduction to ranging and Doppler tracking systems and applications to navigation and geodetic satellites; interferometric systems.
Topic 7: The Global Positioning System.
Comprehensive review of the theory and applications of the Global Positioning System (GPS), including the space segment, the control segment, the user segment, dilution of precision, GPS time, antispoofing, selected availability, differential/kinematic/dynamic techniques, field procedures, and GPS data collection and analysis. Applications of groundbased, aircraftbased, and satellitebased GPS receivers.
196, 296, 396, 496, 596, 796, 896, 996. Special Topics.
For each semester hour of credit earned, the equivalent of one lecture hour a week for one semester. May be repeated for credit. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Space Systems Design.
397. Graduate Seminar.
Student, faculty, and visitor presentations of current research topics. May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing.
Topic 1: Orbital Mechanics Seminar.
Topic 2: Aeronautics Seminar.
Topic 3: Guidance and Control Seminar.
Topic 4: Solids, Structures, and Materials Seminar.
Topic 5: Structural Dynamics Seminar.
197K, 297K, 397K, 497K, 597K, 697K, 797K, 897K, 997K. Research.
For each semester hour of credit earned, one hour of research a week for one semester. May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and consent of instructor.
Topic 1: Research in Experimental Mechanics.
Topic 2: Research in Fluid Mechanics.
Topic 3: Research in Guidance and Control.
Topic 4: Research in Orbital Mechanics.
Topic 5: Research in Solids, Structures, and Materials.
698. Thesis.
The equivalent of three lecture hours a week for two semesters. Offered on the credit/nocredit basis only. Prerequisite: For 698A, graduate standing in aerospace engineering and consent of the graduate adviser; for 698B, Aerospace Engineering 698A.
398R. Master's Report.
Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in aerospace engineering and consent of the graduate adviser.
398T. Supervised Teaching in Aerospace Engineering.
Teaching methods and objectives, criteria for evaluating teaching effectiveness, procedural rules and regulations, laboratory teaching. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and appointment as a teaching assistant.
399R, 699R, 999R. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.
399W, 699W, 999W. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Aerospace Engineering 399R, 699R, or 999R.
