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AERONAUTICS & ASTRONAUTICS

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**A A 101 AIR AND SPACE VEHICLES (5) NW**

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**A A 198 Special Topics in Aeronautics and Astronautics (1-5, max. 10) NW*** Knowlen*

Introduces the field of Aeronautics and Astronautics. Topics include aircraft flight, rocket propulsion, space travel, and contemporary space missions. May include hands-on activities. For non-majors.

View course details in MyPlan: A A 198

**A A 210 Engineering Statics (4) NW**

Applies vector analysis to equilibrium of rigid body systems and subsystems. Includes force and moment resultants, free body diagrams, internal forces, and friction. Analyzes basic structural and machine systems and components. Prerequisite: minimum grade of 2.0 in either MATH 126 or MATH 136; minimum grade of 2.0 in PHYS 121. Offered: AWS.

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**A A 260 Thermodynamics (4) NW**

Introduction to the basic principles of thermodynamics from a macroscopic point of view. Emphasis on the First and Second Laws and the State Principle, problem solving methodology. Prerequisite: minimum grade of 2.0 in either CHEM 140, CHEM 142, CHEM 144, or CHEM 145; minimum grade of 2.0 in either MATH 126, MATH 129, or MATH 136; minimum grade of 2.0 in PHYS 121. Offered: SpS.

View course details in MyPlan: A A 260

**A A 299 Undergraduate Research (1-5, max. 10)**

Research on special topics under the supervision of a faculty member. Application of fundamentals learned in the classroom to real problems in research. Credit/no-credit only. Offered: AWSpS.

View course details in MyPlan: A A 299

**A A 301 Compressible Aerodynamics (4)**

Covers aerodynamics as applied to the problems of performance of flight vehicles in the atmosphere; kinematics and dynamics of flow fields; thin airfoil theory; compressible fluids; one-dimensional compressible flow; and two-dimensional supersonic flow. Prerequisite: either A A 260 or M E 323. Offered: W.

View course details in MyPlan: A A 301

**A A 302 Incompressible Aerodynamics (4)**

Aerodynamics as applied to the problems of performance of flight vehicles in the atmosphere. Kinematics and dynamics of flow fields; incompressible flow about bodies. Thin airfoil theory; finite wing theory. Prerequisite: minimum grade of 1.7 in A A 301; PHYS 123; either AMATH 351, MATH 136, or MATH 307. Offered: Sp.

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**A A 310 Orbital and Space Flight Mechanics (4)**

Newton's law of gravitation. Two-body problem, central force motion, Kepler's laws. Trajectories and conic sections. Position and velocity as functions of time. Orbit determination and coordinate transformations. Rocket dynamics, orbital maneuvers, Hohmann transfer. Interplanetary trajectories, patched conics. Planetary escape and capture. Gravity assist maneuvers. Prerequisite: M E 230. Offered: A.

View course details in MyPlan: A A 310

**A A 311 Atmospheric Flight Mechanics (4)**

Applied aerodynamics, aircraft flight "envelope," minimum and maximum speeds, climb and glide performance. Range and endurance, take-off and landing performance, using both jet and propeller power plants. Longitudinal and dynamic stability and control, wing downwash, stabilizer and elevator effectiveness, power effects. Lateral and directional stability and control. Prerequisite: M E 230 Offered: A.

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**A A 312 Structural Vibrations (4)**

Vibration theory. Characteristics of single and multi degree-of-freedom linear systems with forced inputs. Approximate methods for determining principal frequencies and mode shapes. Application to simple aeroelastic problems. Prerequisite: M E 230. Offered: W.

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**A A 320 Aerospace Instrumentation (3)**

Hands-on laboratory experience for understanding the design and function of electronic circuits and instrumentation utilized in aerospace engineering. Topics include Ohm's law, Kirchoff's laws, DC and AC circuits, passive and active components, op-amps and comparators, sensors, signal conditioning, electromechanical systems and actuators, digital systems, and data acquistion. Prerequisite: PHYS 123. Offered: A.

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**A A 321 Aerospace Laboratory I (3)**

The design and conduct of experimental inquiry in the field of aeronautics and astronautics. Laboratory experiments on supersonic flow, structures, vibrations, material properties, and other topics. Theory, calibration, and use of instruments, measurement techniques, analysis of data, report writing. Prerequisite: A A 311; and A A 320 Offered: W.

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**A A 322 Aerospace Laboratory II (3)**

Design and conduct of experimental inquiry in the field of aeronautics and astronautics. Student groups propose, design, build, and conduct laboratory experiments in one of the following broad topic areas: aerodynamics, structures, propulsion, or energetics. Results are presented in written and oral reports. Prerequisite: minimum grade of 1.7 in A A 321. Offered: Sp.

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**A A 331 Aerospace Structures I (4)**

Analysis and design of aerospace structures. Reviews concepts of stress, strain, and equations of elasticity. Plane stree and plane strain. Application to aerospace structural elements including general bending and torsion of rods and beams, and open and closed thin-walled structures and box beams. Prerequisite: CEE 220. Offered: W.

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**A A 332 Aerospace Structures II (4)**

Shear flow in multi-cell thin walled sections.Bending of rectangular and circular plates. Buckling analysis of beams and plates. Energy principles in elasticity. Introduction to the finite element method. Elements of fracture mechanics and fatigue. Prerequisite: minimum grade of 1.7 in A A 331. Offered: Sp.

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**A A 360 Propulsion (4)**

Study of the aero- and thermodynamics of jet and rocket engines. Air-breathing engines as propulsion systems. Turbojets, turbofans, turboprops, ramjets. Aerodynamics of gas-turbine engine components. Rocket vehicle performance. Introduction to space propulsion. Prerequisite: minimum grade of 1.7 in A A 301. Offered: Sp.

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**A A 400 Gas Dynamics (3)**

Introduction to kinetic theory and free molecule flow. Review of thermodynamics. One-dimensional gas dynamics: one-dimensional wave motion, combustion waves. Ideal and real gas application. Prerequisite: PHYS 123; either A A 260 or CHEM E 260. Offered: W.

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**A A 402 Fluid Mechanics (3)**

Introduction to fluid mechanics, dimensional analysis, effects of gravity on pressure, kinematics, conservation of mass and momentum, control-volume method, conservation of energy, vorticity and viscosity, viscous effects, Navier-Stokes solutions, and boundary layers. Prerequisite: MATH 324; A A 301. Offered: A.

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**A A 405 Introduction to Aerospace Plasmas (3)**

Development of introductory electromagnetic theory including Lorentz force and Maxwell's equations. Plasma description. Single particle motions and drifts in magnetic and electric fields. Derivation of plasma fluid model. Introduction to plasma waves. Applications to electric propulsion, magnetic confinement, and plasmas in space and Earth's outer atmosphere. Prerequisite: PHYS 123; MATH 324. Offered: A.

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**A A 410 Aircraft Design I (4-)**

Conceptual design of a modern airplane to satisfy a given set of requirements. Estimation of size, selection of configuration, weight and balance, and performance. Satisfaction of stability, control, and handling qualities requirements. Prerequisite: A A 320; A A 311; A A 332; and A A 360 Offered: W.

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**A A 411 Aircraft Design II (-4)**

Preliminary design of a modern airplane to satisfy a given set of requirements. Estimation of size, selection of configuration, weight and balance, and performance. Satisfaction of stability, control, and handling qualities requirements. Prerequisite: A A 410. Offered: Sp.

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**A A 419 Aerospace Heat Transfer (3)**

Fundamentals of conductive, convective, and radiative heat transfer with emphasis on applications to atmospheric and space flight. Prerequisite: PHYS 123; MATH 307. Offered: W.

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**A A 420 Spacecraft and Space Systems Design I (4-)**

Design of space systems and spacecraft for advanced near-Earth and interplanetary missions. Astrodynamics, space environment, space systems engineering. Mission design and analysis, space vehicle propulsion, flight mechanics, atmospheric entry, aerobraking, configuration, structural design, power systems. thermal management, systems integration. Oral presentations and report writing. Design topics vary. Prerequisite: A A 301; A A 310; A A 332; and A A 360. Offered: W.

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**A A 421 Spacecraft and Space System Design II (-4)**

A continuation of A A 420. Course content varies from year to year and is dependent on the design topic chosen for A A 420. Prerequisite: A A 420. Offered: Sp.

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**A A 430 Finite Element Analysis in Aerospace (3)**

Introduction to the finite element method and application. One-, two-, and three-dimensional problems including trusses, beams, box beams, plane stress and plane strain analysis, and heat transfer. Use of finite element software. Prerequisite: CEE 220. Offered: A.

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**A A 432 Composite Materials for Aerospace Structures (3)**

Introduction to analysis and design of aerospace structures utilizing filamentary composite materials. Basic elastic properties and constitutive relations of composite laminates. Failure criteria, buckling analysis, durability, and damage tolerance of composite structures. Aerospace structure design philosophy and practices. Prerequisite: A A 332. Offered: W.

View course details in MyPlan: A A 432

**A A 440 Flight Mechanics I (3)**

Calculation of aerodynamic characteristics of aircraft and components including stability derivatives. Relation to wind tunnel and flight data. Vehicle equations of motion within the atmosphere, characteristics of propulsion systems and components including propellers. Prediction of performance, stability, and control characteristics for a specific aircraft. Prerequisite: A A 311; A A 312; and A A 447. Offered: W.

View course details in MyPlan: A A 440

**A A 441 Flight Test Engineering (3)**

Determination in flight of performance, stability, and control characteristics of aircraft; and comparison with predicted and wind tunnel results. Prerequisite: A A 311; A A 440. Offered: Sp.

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**A A 447 Control in Aerospace Systems (4)**

Overview of feedback control. Dynamic models for control systems design including ODE, transfer function, and state-space. Linearization of nonlinear models. Analysis of stability, controllability, observability, time/frequency domain techniques. Frequency of response design techniques. Design of control systems via case studies. Prerequisite: minimum grade of 1.7 in A A 312; M E 230; MATH 308. Offered: A.

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**A A 448 Control Systems Sensors and Actuators (3)**

Overview of feedback control. Study of control systems components and formulation of their mathematical models. Discussion and analysis of amplifiers, DC servomotors, magnetic-actuators, accelerometers, potentiometers, shaft encoders and resolvers, proximity sensors, and force transducers.Experimental determination of component models and model parameters. Two three-hour laboratories per week. Prerequisite: A A 447.

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**A A 449 Special Topics in Controls (3-5)**

Topics of current interest in controls. Offered: Sp.

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**A A 461 Advanced Air Breathing Propulsion (3)**

Examines gas turbine engine design methodology. Covers aerodynamics or gas dynamics of air breathing engine components: inlets, compressors, turbines, and nozzles. Studies the on-design and off-design performance of gas turbine engines. Includes combustion, emissions, noise, and advanced air breathing propulsion systems. Prerequisite: A A 360. Offered: A.

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**A A 462 Rocket Propulsion (3)**

Covers the physical and performance characteristics of chemical rocket propulsion systems. Includes combustion chamber thermochemistry, propellant properties and handling, and rocket system component interactions. Prerequisite: A A 260. Offered: Sp.

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**A A 470 Systems Engineering (4)**

Concepts of system approach, system hierarchies, functional analysis, requirements, trade studies, and other concepts used to define and integrate complex engineering systems. Introduction to risk analysis and reliability, failure modes and effects analysis, writing specifications, and lean manufacturing. Offered: jointly with IND E 470; A.

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**A A 480 Systems Dynamics (3)**

Equations of motion and solutions for selected dynamic problems; natural frequencies and mode shapes; response of simple systems to applied loads. Prerequisite: A A 312. Offered: Sp.

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**A A 496 Undergraduate Seminar (1, max. 4)**

Lectures and discussions on topics of current interest in aviation and space technology by guest speakers. Topics vary. Credit/no-credit only. Offered: W.

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**A A 498 Special Topics (1-5, max. 15)**

Topics of current interest in the Department of Aeronautics and Astronautics.

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**A A 499 Undergraduate Research (1-5, max. 10)**

Research on special topics under the supervision of a faculty member. Application of fundamentals learned in the classroom to real problems in research. A maximum of 6 credits may be applied toward senior technical electives. Offered: AWSpS.

View course details in MyPlan: A A 499

**A A 501 Physical Gasdynamics I (3)**

Equilibrium kinetic theory; chemical thermodynamics; thermodynamic properties derived from quantum statistical mechanics; reacting gas mixtures; applications to real gas flows and gas dynamics. Offered: W, odd years.

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**A A 503 Continuum Mechanics (3)**

Reviews concepts of motion, stress, energy for a general continuum; conservation of mass, momentum, and energy; and the second law; constitutive equations for linear/nonlinear elastic, viscous/inviscid fluids, and general materials; and examples/solutions for solid/fluid materials. Offered: jointly with M E 503; A.

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**A A 504 Compressible Fluid Mechanics (3)**

Reviews the fundamentals with application to external and internal flows; supersonic flow, 1D and Quasi-1D, steady and unsteady flow, oblique shocks and expansion waves, linearized flow, 2D flow, method of characteristics; and transonic and hypersonic flow. Offered: A.

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**A A 506 Vortex-Dominated Flows (3)**

Examines the vorticity equation, baroclinic torque, solenoidality, Biot-Savart's formula, diffusion of vorticity, Burger vortex, system of vortices, Kelvin-Helmholtz instability, effects of density, shear, and surface tension on instability, swirling flows, and other special topics. Offered: Sp, even years.

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**A A 507 Fluid Mechanics (3)**

Covers inviscid and viscous imcompressible flows, exact solutions of laminar flows, creeping flows, boundary layers, free-shear flows, vorticity equation, and introduction to vortex dynamics. Offered: jointly with M E 507; W.

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**A A 508 Turbulence (3)**

The phenomena of turbulence; transition prediction; Reynolds stresses; turbulent boundary-layer equations. Approximate methods for turbulent boundary layers. Prerequisite: A A/M E 507 or permission of instructor. Offered: Sp, odd years.

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**A A 510 Mathematical Foundations of Systems Theory (4)**

Mathematical foundations for system theory presented from an engineering viewpoint. Includes set theory; functions, inverse functions; metric spaces; finite dimensional linear spaces; linear operators on finite dimensional spaces; projections on Hilbert spaces. Applications to engineering systems stressed. Offered: jointly with CHEM E 510/E E 510/M E 510.

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**A A 516 Stability and Control of Flight Vehicles (3)**

Static and dynamic stability and control of flight vehicles in the atmosphere. Determination of stability derivatives. Effects of stability derivatives on flight characteristics. Flight dynamic model. Responses to control inputs and external disturbances. Handling qualities. Control system components, sensor characteristics. Stability augmentation systems. Offered: A.

View course details in MyPlan: A A 516

**A A 518 Automatic Control of Flight Vehicles (3)**

Specifications of flight vehicle performance. Synthesis of stability augmentation systems and autopilot control laws in the frequency-domain and using multivariable control methods. Reduced-order controller synthesis, digital design, and implementation. Use of computer-aided control design packages. Prerequisite: A A 516 and A A 548. Offered: Sp, odd years.

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**A A 523 Special Topics in Fluid Physics (3)**

Offered: AWSp.

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**A A 524 Aeroacoustics (3)**

Reviews the fundamental concepts of acoustics which include sound measurements, reflection, resonance, transmission, radiation, scattering, diffraction, ray acoustics, wave guide, turbo-machinery noise, sound suppression, jet noise, and airframe noise and acoustic problems in rockets and other propulsion systems. Offered: A, odd years.

View course details in MyPlan: A A 524

**A A 525 Special Topics in Advanced Airbreathing Engines (3)**

Reviews the fundamental concepts of advanced airbreathing engines including advanced gas turbines, ramjets, scramjets and variants, detonations engines, flow with chemical energy release, shock dynamics, Chapman-Jouguet, ZND model, and multi-cellular and spinning detonation. Offered: W, even years.

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**A A 527 Space Power Systems (3)**

Explores the theoretical background and technology of power systems for satellites, space science missions, and planetary and lunar outposts. Focuses on photovoltaic, solar-thermal, and nuclear systems, as well as chemical systems for storage. Addresses thermal management. Offered: A, even years.

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**A A 528 Spacecraft Dynamics and Control (3)**

Examines spacecraft dynamics and control. Includes basic orbital mechanics - the restricted three body problem, Hill's theory, perturbation theory, orbit determination, rigid body kinematics and dynamics, attitude control, and spacecraft formation flying. Prerequisite: MATH 307; MATH 308. Offered: W, odd years.

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**A A 529 Space Propulsion (3)**

Nucleonics, and heat transfer of nuclear-heated rockets. Electrothermal, electromagnetic, and electrostatic thrusters. Power/propulsion systems. Prerequisite: permission. Offered: Sp, odd years.

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**A A 530 Mechanics of Solids (3)**

General concepts and theory of solid mechanics. Large deformations. Behavior of elastic, viscoelastic, and plastic solids. Linear theory of elasticity and thermoelasticity. Wave propagation in solids. Offered: A.

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**A A 532 Mechanics of Composite Materials (3)**

Analysis and design of composite materials for aerospace structures. Micromechanics. Anisotropic elasticity. Laminated plate theory. Thermo-viscoelastic behavior and fracture of composites. Prerequisite: coursework in mechanics of matierals or permission of instructor. Offered: A.

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**A A 535 Advanced Composite Structural Analysis (3)**

Covers advanced stress analysis methods for composite structures made of beams, laminates, sandwich plates, and thin shells; stress and buckling analyses of solid and thin-walled composite beams; shear deformable theory for bending of thick laminated plates; and stress and fracture mechanics analysis of bonded joints. Prerequisite: A A 532. Offered: jointly with M E 500; Sp, odd years.

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**A A 538 Introduction to Structural Optimization (3)**

Includes the formulation of engineering design problems as optimization problems, gradient based numerical optimization methods, design oriented structural analysis, structural sensitivity analysis, approximation concepts, and introduction to multidisciplinary design optimization. Prerequisite: coursework in structural analysis; finite elements; and computer programming; or permission of instructor. Offered: A, odd years.

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**A A 540 Finite Element Analysis I (3)**

Formulation of the finite element method using variational and weighted residual methods. Element types and interpolation functions. Application to elasticity problems, thermal conduction, and other problems of engineering and physics. Offered: W.

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**A A 541 Finite Element Analysis II (3)**

Advanced concepts of the finite element method. Hybrid and boundary element methods. Nonlinear, eigenvalue, and time-dependent problems. Prerequisite: A A 540 or permission of instructor. Offered: Sp.

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**A A 543 Computational Fluid Dynamics (3)**

Examines numerical discretization of the inviscid compressible equations of fluid dynamics; finite-difference and finite-volume methods; time integration, iterative methods, and explicit and implicit algorithms; consistency, stability, error analysis, and properties of numerical schemes, grid generation; and applications to the numerical solution of model equations and the 2D Euler equations. Offered: W.

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**A A 544 Turbulence Modeling and Simulation (3)**

Examines numerical discretization of the incompressible Navier-Stokes equation; projection method, introduction to turbulence; Reynolds Averaged Navier-Stokes equations; algebraic, one-equation, and two-equation turbulence models; large-eddy simulation; direct numerical simulation; and applications to the numerical solution of laminar and turbulent flows in simple geometries. Offered: Sp.

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**A A 545 Computational Methods for Plasmas (3)**

Develops the governing equations for plasma models - particle, kinetics, and MHD. Applies the governing equation to plasma dynamics through the PIC method and integration of fluid evaluation equations. Examines numerical solution to equilibrium configurations, and linear stability by energy principle and variational method. Prerequisite: A A 405 or A A 557. Offered: Sp, odd years.

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**A A 546 Advanced Topics in Control System Theory (3)**

Topics of current interest for advanced graduate students with adequate preparation in linear and nonlinear system theory. Prerequisite: permission of instructor.

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**A A 547 Linear Systems Theory (4)**

Linearity, linearization, finite dimensionality, time-varying vs. time-invariant linear systems, interconnection of linear systems, functional/structural descriptions of linear systems, system zeros and invertibility, linear system stability, system norms, state transition, matrix exponentials, controllability and observability, realization theory. Offered: jointly with E E 547/M E 547.

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**A A 548 Linear Multivariable Control (3)**

Introduction to MIMO systems, successive single loop design comparison, Lyapunov stability theorem, full state feedback controller design, observer design, LQR problem statement, design, stability analysis, and tracking design. LQG design, separation principle, stability robustness. Prerequisite: A A 547/E E 547/M E 547. Offered: jointly with E E 548/M E 548.

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**A A 549 Estimation and System Identification (3)**

Fundamentals of state estimation for linear and nonlinear systems. Discrete and continuous systems. Probability and stochastic systems theory. Models with noise. Kalman-Bucy filters, extended Kalman filters, recursive estimation. Numerical issues in filter design and implementation. Prerequisite: either A A 547, E E 547, or M E 547. Offered: jointly with E E 549/M E 549.

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**A A 550 Nonlinear Optimal Control (3)**

Calculus of variations for dynamical systems, definition of the dynamic optimization problem, constraints and Lagrange multipliers, the Pontryagin Maximum Principle, necessary conditions for optimality, the Hamilton-Jacobi-Bellman equation, singular arc problems, computational techniques for solution of the necessary conditions. Offered: jointly with E E 550/M E 550.

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**A A 553 Vibrations of Aerospace Systems (3)**

Continuous and discrete systems, natural frequencies, and modal analysis; forced vibrations and motion-dependent forces. Structural damping; control augmented structures. Measurements for structural dynamic testing. Prerequisite: A A 571 or equivalent. Offered: Sp, odd years.

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**A A 554 Aeroelasticity (3)**

Static and dynamic aeroelasticity, unsteady aerodynamics, aeroservoelastic modeling, and active control. Offered: A, even years.

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**A A 556 Space and Laboratory Plasma Physics (3)**

Discussion of waves, equilibrium and stability, diffusion and resistivity, basic plasma kinetic theory, and wave-particle interactions. Prerequisite: ESS 415, or equivalent, or permission of instructor. Offered: jointly with ESS 576; W, odd years.

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**A A 557 Physics of Fusion Plasmas (3)**

Review and comparison of single particle and fluid descriptions of plasmas. MDH equilibrium, flux surfaces, and basic toroidal description. Collisional processes including physical and velocity space diffusion. Introduction to island formation, stochasticity, and various plasma instabilities. Prerequisite: A A 405 or GPHYS 505. Offered: W, even years.

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**A A 558 Plasma Theory (3)**

Equilibrium, stability, and confinement. Classical transport, collisionless and resistive skin depths. Ideal MHD equations formally derived and properties of plasmas in the ideal limit are studied. Straight and toroidal equilibrium. Linear stability analysis with examples. Taylor minimum energy principle. Prerequisite: either A A 405, A A 556, A A 557, ESS 576, or GPHYS 537. Offered: Sp, even years.

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**A A 559 Plasma Science Seminar (1, max. 30)**

Current topics in plasma science and controlled fusion with presentations by invited speakers, on-campus speakers, and students. Students expected to give a seminar once or twice a year with instructor reviewing the method of presentation and material used for the presentation. Credit/no-credit only. Offered: AWSp.

View course details in MyPlan: A A 559

**A A 560 Plasma Diagnostics (3)**

Discusses plasma measurement methods including material probes and optical methods. Covers techniques for making measurement in a high electrical noise environment. Presents methods for measuring electron and ion temperatures, density, impurities, magnetic fields, fluctuations, and neutrals. Prerequisite: A A 405 or equivalent. Offered: A, even years.

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**A A 564 Kinetic Theory/Radiative Transfer (3)**

Boltzmann and Collisionless Boltzmann (Vlasov) equations. Instabilities in homogeneous and inhomogeneous plasma, quasi-linear diffusion, wave-particle interaction, collisional (Fokker-Plank) equation. Introduction to radiative non-equilibrium, scattering and absorption processes. Integral equation of radiative transfer. Prerequisite: A A 501 or permission of instructor. Offered: Sp, even years.

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**A A 565 Fusion Reactor Fundamentals (3)**

Introduction to basic engineering features of fusion power plants. Brief description of basic fusion physics and discussion of power plants for leading thermonuclear concepts. Engineering problems; blanket, shield neutronics; materials, thermal hydraulics; tritium, superconducting systems. Prerequisite: completion of or concurrent enrollment in A A 405 or permission of instructor. Offered: W, odd years.

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**A A 570 Manifolds and Geometry for Systems and Control (3)**

Introduction to fundamentals of calculus on manifolds and group theory with applications in robotics and control theory. Topics include: manifolds, tangent spaces and bundles, Lie groups and algebras, coordinate vs. coordinate-free representations. Applications from physics, robotics, and control theory. Offered: jointly with E E 570/M E 570; W, even years.

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**A A 571 Principles of Dynamics I (3)**

Systems of particles, rotating axes, rigid-body dynamics; calculus of variations. Lagrangian mechanics. Hamilton's principle. Kane's equations. Periodic and quasiperiodic motion. Stability of dynamical systems. Offered: A.

View course details in MyPlan: A A 571

**A A 578 Convex Optimization (4)**

Basics of convex analysis: Convex sets, functions, and optimization problems. Optimization theory: Least-squares, linear, quadratic, geometric and semidefinite programming. Convex modeling. Duality theory. Optimality and KKT conditions. Applications in signal processing, statistics, machine learning, control communications, and design of engineering systems. Prerequisite: A A 510, CHEM E 510, E E 510 or M E 510. Offered: jointly with E E 578/M E 578; W.

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**A A 580 Geometric Methods for Non-Linear Control Systems (3)**

Analysis and design of nonlinear control systems focusing on differential geometric methods. Topics include controllability, observability, feedback linearization, invariant distributions, and local coordinate transformations. Emphasis on systems evolving on Lie groups and linearly uncontrollable systems. Offered: jointly with E E 580/M E 580; Sp, even years.

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**A A 581 Digital Control System Design (4)*** M. BERG*

Digital control system design by classical methods. Discrete-time systems and the z-transform. Modeling sampled-data systems. Frequency response of discrete time systems and aliasing. Nyquist stability criterion and gain and phase margins. Discrete-time control law determination by direct z-plane root locus and loop shaping methods. Includes hands-on-with-hardware projects. Prerequisite: AA/EE 447 or ME 471. Offered: jointly with E E 581/M E 581; W.

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**A A 582 Introduction to Discrete Event Systems (3)**

Modeling DES with automata and Petri nets. Languages. State estimation and diagnostics. Control specifications. Feedback control. Dealing with uncontrollability and unobservability. Dealing with blocking. Timed automata and Petri nets. Prerequisite: A A 447/E E 447/ M E 471. Instructors: Berg Offered: jointly with E E 582/M E 582; Sp, even years.

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**A A 583 Nonlinear Control Systems (3)**

Analysis of nonlinear systems and nonlinear control system design. Phase plane analysis. Lyapunov stability analysis. Describing functions. Feedback linearization. Introduction to variable structure control. Prerequisite: A A 447/E E 447/M E 471. Offered: jointly with E E 583/M E 583.

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**A A 585 System Identification and Adaptive Control (3)**

Theory and methods of system identification and adaptive control. Identification of linear-in-parameter systems, using recursive LS and extended LS methods; model order selection. Indirect and direct adaptive control. Controller synthesis, transient and stability properties. Offered: jointly with E E 585/M E 585.

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**A A 589 Special Topics in Solid Mechanics (4)**

Offered: AWSp.

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**A A 591 Robotics and Control Systems Colloquium (1, max. 30)**

Colloquium on current topics in robotics and control systems analysis and design. Topics presented by invited speakers as well as on-campus speakers. Emphasis on the cross-disciplinary nature of robotics and control systems. Credit/no-credit only. Offered: jointly with CHEM E 591/E E 591/M E 591.

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**A A 593 Feedforward Control (3)**

Design feedforward controllers for precision output tracking; inversion-based control of non-minimum-phase systems; effect of plant uncertainty on feedforward control; design of feedforward controllers for applications such as vertical take off and landing aircraft, flexible structures and piezo-actuators. Prerequisite: A A 547/E E 547/M E 547. Instructors: Devasia Offered: jointly with E E 593/M E 593; Sp, even years.

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**A A 594 Robust Control (3)**

Basic foundations of linear analysis and control theory, model realization and reduction, balanced realization and truncation, stabilization problem, coprime factorizations, Youla parameterization, matrix inequalities, H-infinity and H2 control, KYP lemma, uncertain systems, robust H2, integral quadratic constraints, linear parameter varying synthesis, applications of robust control. Prerequisite: A A 547/E E 547/M E 547. Offered: jointly with E E 594/M E 594; Sp, odd years.

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**A A 595 Global Integrated Systems Engineering ([4/5]-, max. 9)*** C. MASTRANGELO*

Covers systems engineering, project management, finance and economics in a global environment. Offered: jointly with IND E 595; AW.

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**A A 596 Global Integrated Systems Engineering Project (3)**

Project-based systems design course. Prerequisite: A A/INDE 595. Instructors: Mastrangelo Offered: jointly with IND E 596; Sp.

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**A A 597 Networked Dynamics Systems (3)**

Provides an overview of graph-theoretic techniques that are instrumental for studying dynamic systems that coordinate their states over a signal-exchange network. Topics include network models, network properties, dynamics over networks, formation control, biological networks, observability, controllability, and performance measures over networks. Prerequisite: A A 547/E E 547/M E 547. Offered: jointly with E E 597/M E 597.

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**A A 598 Special Topics in Aeronautics and Astronautics (1-5, max. 30)**

Introduction of special topics in the field of aeronautics and astronautics. Topics introduced by regular and guest speakers and includes a variety of information that is of current interest in aeronautics and astronautics. Offered: AWSp.

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**A A 599 Special Projects (1-5, max. 30)**

Investigation on a special project by the student under the supervision of a faculty member. Offered: AWSpS.

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**A A 600 Independent Study or Research (*-)**

Offered: AWSpS.

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**A A 700 Master's Thesis (*-)**

Offered: AWSpS.

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**A A 800 Doctoral Dissertation (*-)**

Offered: AWSpS.

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