# Aerospace

**Ae 100. Research in Aerospace. ***Units to be arranged in accordance with work accomplished. *Open to suitably qualified undergraduates and first-year graduate students under the direction of the staff. Credit is based on the satisfactory completion of a substantive research report, which must be approved by the Ae 100 adviser and by the option representative.

**Ae/APh/CE/ME 101 abc. ***Fluid Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisites: APh 17 or ME 11 abc, and ME 12 or equivalent, ACM 95/100 or equivalent (may be taken concurrently). *Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli’s equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics. Instructors: Pullin, Colonius

**Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. ***9 units (3-0-6); first, second, third terms. Prerequisites: ME 12 abc. *Introduction to continuum mechanics: kinematics, balance laws, constitutive laws with an emphasis on solids. Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Wave propagation. Analysis of rods, plates and shells with applications in a variety of fields. Variational theorems and approximate solutions. Elastic stability. Instructors: Lapusta, Ortiz, Ravichandran.

**Ae 103 abc. Dynamics and Control of Aircraft and Spacecraft. ***9 units (3-0-6); first, second, third terms. Prerequisites: ACM 104 and ACM 100ab (may be taken concurrently). *Advanced spacecraft and aircraft dynamics. Guidance, navigation, and control of autonomous aerospace vehicles. Optimal control theory and state estimation for aerospace autonomy. Instructors: Chung, Murray.

**Ae/APh 104 abc. Experimental Methods. ***9 units (3-0-6) first term; (0-**6-3) second, third terms. Prerequisites: ACM 95/100 ab or equivalent (may be taken concurrently), Ae/APh/CE/ME 101 abc or equivalent (may be taken concurrently). *Lectures on experiment design and implementation. Measurement methods, transducer fundamentals, instrumentation, optical systems, signal processing, noise theory, analog and digital electronic fundamentals, with data acquisition and processing systems. Experiments (second and third terms) in solid and fluid mechanics with emphasis on current research methods. Instructor: Gharib.

**Ae 105 abc. Aerospace Engineering. ***9 units (3-0-6) first term, (2-4-3) second term, (0-8-1) third term; first, second, third terms. Prerequisites: ME 11 abc and ME 12 abc or equivalent. *Part a: Introduction to spacecraft systems and subsystems, mission design, fundamentals of orbital and rocket mechanics, launch vehicles and space environments; JPL-assisted design exercise; spacecraft mechanical, structural, and thermal design; numerical modeling, test validation. Part b: Introduction to guidance, navigation, and control (GNC), measurement systems, Kalman filtering, system analysis, simulation, statistical error analysis, case studies of GNC applications; preliminary discussion and setup for team project leading to system requirements review. Part c: Team project leading to preliminary design review and critical design review. Instructors: Klesh, Scharf, Alvarez-Salazar .

**CE/Ae/AM 108 ab. Computational Mechanics. ***9 units (3-5-1). *For course description, see Civil Engineering.

**Ae 115 ab. Spacecraft Navigation. ***9 units (3-0-6); first, second terms. Prerequisite: CDS 110 a. *This course will survey all aspects of modern spacecraft navigation, including astrodynamics, tracking systems for both low-Earth and deep-space applications (including the Global Positioning System and the Deep Space Network observables), and the statistical orbit determination problem (in both the batch and sequential Kalman filter implementations). The course will describe some of the scientific applications directly derived from precision orbital knowledge, such as planetary gravity field and topography modeling. Numerous examples drawn from actual missions as navigated at JPL will be discussed. Not offered 2017–18.

**APh/Ph/Ae 116. Physics of Thermal and Mass Transport in Hydrodynamic Systems. ***12 units (3-0-9), second term. *For course description, see Applied Physics.

**Ae/ME 118. Classical Thermodynamics. ***9 units (3-0-6); first term. Prerequisites: ME 11 abc, ME 12, or equivalent. ***F**undamentals of classical thermodynamics. Basic postulates and laws of thermodynamics, work and heat, entropy and available work, and thermal systems. Equations of state, compressibility functions, and the Law of Corresponding States. Thermodynamic potentials, chemical and phase equilibrium, phase transitions, and thermodynamic properties of solids, liquids, and gases. Examples will be drawn from fluid dynamics, solid mechanics, and thermal science applications. Minnich.

**Ae/ME 120 ab. Combustion Fundamentals. ***9 units (3-0-6); second, third terms. Prerequisite: ME 119 a or equivalent. *The course will cover thermodynamics of pure substances and mixtures, equations of state, chemical equilibrium, chemical kinetics, combustion chemistry, transport phenomena, and the governing equations for multicomponent gas mixtures. Topics will be chosen from non-premixed and premixed flames, the fluid mechanics of laminar flames, flame mechanisms of combustion-generated pollutants, and numerical simulations of multicomponent reacting flows. Instructor: Not offered 2017–18.

**Ae 121 abc. Space Propulsion. ***9 units (3-0-6); first, second, third terms. Open to all graduate students and to seniors with instructor’s permission. *Ae 121 is designed to introduce the fundamentals of chemical, electric and

advanced propulsion technologies. The course focuses on the thermochemistry and aerodynamics of chemical and electrothermal propulsion systems, the physics of ionized gases and electrostatic and electromagnetic processes in electric thrusters. These analyses provide the opportunity to introduce the basic concepts of non-equilibrium gas dynamics and kinetic theory.

Specific technologies such as launch vehicle rocket engines, monopropellant engines, arcjets, ion thrusters, magnetoplasmadynamic engines and Hall thrusters will be discussed. Ae 121 also provides an introduction to advanced propulsion concepts such as solar sails and antimatter rockets. Instructor: Polk.

**Ae 150 abc. Aerospace Engineering Seminar. ***1 unit; first, second, third terms. *Speakers from campus and outside research and manufacturing organizations discuss current problems and advances in aerospace engineering. Graded pass/fail. Instructor: Meiron.

**EE/Ae 157 ab. Introduction to the Physics of Remote Sensing. ***9 units (3-0-6); first, second terms. *For course description, see Electrical Engineering.

**Ae 159. Space Optical System Engineering. ***9 units (3-0-6); third term. Prerequisites: Ph 2, EE/Ae 157, or equivalent; APh 23 desirable. *Introduction to optical system engineering for remote sensing from space will be presented. End-to-end optical systems are discussed within the framework of the 10 scientific/technical disciplines required to build a successful system: optical engineering, physical optics of materials, solid-state physics/detectors, mechanics and mechanisms engineering, wavefront sensing and control, structures and dynamics, thermal engineering, spacecraft engineering, psychology of vision and software processing of images, and end-to-end system validation and calibration. Emphasis will be on the development of optical engineering tools. Instructor: Breckenridge.

**Ae/Ge/ME 160 ab. Continuum Mechanics of Fluids and Solids. ***9 units (3-0-6); first, second terms. *Elements of Cartesian tensors. Configurations and motions of a body. Kinematics—study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics—balance laws. Linear and angular momentum, force, traction stress. Cauchy’s theorem, properties of Cauchy’s stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff ) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. Instructors: Lapusta, Bhattacharya.

**Ae/CE 165 ab. Mechanics of Composite Materials and Structures. ***9 units (2-2-5); first, second terms. Prerequisite: Ae/AM/CE/ME 102 a. *Introduction and fabrication technology, elastic deformation of composites, stiffness bounds, on- and off-axis elastic constants for a lamina, elastic deformation of multidirectional laminates (lamination theory, ABD matrix), effective hygrothermal properties, mechanisms of yield and failure for a laminate, strength of a single ply, failure models, splitting and delamination. Experimental methods for characterization and testing of composite materials. Design criteria, application of design methods to select a suitable laminate using composite design software, hand layup of a simple laminate and measurement of its stiffness and thermoelastic coefficients. Pellegrino.

**Ae 200. Advanced Research in Aerospace. ***Units to be arranged. *Ae.E. or Ph.D. thesis level research under the direction of the staff. A written research report must be submitted during finals week each term.

**Ae 201 a. Advanced Fluid Mechanics. ***9 units (3-0-6); second term. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent; AM 125 abc or ACM 101 (may be taken concurrently). *Foundations of the mechanics of real fluids. Basic concepts will be emphasized. Subjects covered will include a selection from the following topics: physical properties of real gases; the equations of motion of viscous and inviscid fluids; the dynamical significance of vorticity; vortex dynamics; exact solutions; motion at high Reynolds numbers; hydrodynamic stability; boundary layers; flow past bodies; compressible flow; subsonic, transonic, and supersonic flow; shock waves. Instructor: Meiron.

**Ae 204 ab. Technical Fluid Mechanics. ***9 units (3-0-6); second, third terms. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent. *External and internal flow problems encountered in engineering, for which only empirical methods exist. Turbulent shear flow, separation, transition, three-dimensional and nonsteady effects. Basis of engineering practice in the design of devices such as mixers, ejectors, diffusers, and control valves. Studies of flow-induced oscillations, wind effects on structures, vehicle aerodynamics. Not offered 2017–18.

**Ae 205 ab. Advanced Space Project. ***9 units (2-4-3); second, third terms. Prerequisites: Ae105 abc. *This is an advanced course on the design and implementation of space projects and it is currently focused on the flight project Autonomous Assembly of a Reconfigurable Space Telescope (AAReST). The objective is to be ready for launch and operation in 2015. Each student will be responsible for a specific activity, chosen from the following: optimization of telescope system architecture; design, assembly and testing of telescope optics; telescope calibration procedure and algorithms for wavefront control; thermal analysis; boom design and deployment test methods; effects of spacecraft dynamics on telescope performance; environmental testing of telescope system. Each student will prepare a survey of the state of the art for the selected activity, and then develop a design/ implementation plan, execute the plan and present the results in a final report. Instructor: Pellegrino.

**Ae 208 abc. GALCIT Colloquium. ***1 unit; first, second, third terms. *A seminar course in fluid, solid, space, and bio mechanics. Weekly lectures on current developments are presented by staff members, graduate students, and visiting scientists and engineers. Graded pass/fail. Instructors: Austin, Chung.

**Note: **The following courses, with numbers greater than 209, are one-, two-, or three-term courses offered to interested students. Depending on conditions, some of the courses may be taught as tutorials or reading courses, while others may be conducted more formally.

**Ae/AM/MS/ME 213. Mechanics and Materials Aspects of Fracture. ***9 units (3-0-6); second term. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and instructor’s permission. *Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elastic-plastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, “dynamic” stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Instructor: Not offered 2017–18.

**Ae/AM/CE/ME 214 ab. Computational Solid Mechanics. ***9 units (3-5-1); first, second terms. Prerequisites: ACM 100 ab or equivalent; CE/AM/Ae 108 ab or equivalent or instructor’s permission; Ae/AM/CE/ME 102 abc or Ae/ Ge/ME 160 ab or instructor’s permission. *Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. First term: Variational principles. Finite element analysis. Variational problems in linear and finite kinematics. Time integration, initial boundary value problems. Elasticity and inelasticity. Constitutive modeling. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Second term: Multiscale modeling strategies. Computational homogenization in linear and finite kinematics. Spectral methods. Atomistic modeling and atomistic-to-continuum coupling techniques. Not offered 2017–18.

**Ae/AM/ME 215. Dynamic Behavior of Materials. ***9 units (3-0-6); second term. Prerequisites: ACM 100 abc or AM 125 abc; Ae/AM/CE/ME 102 abc. *Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Not offered 2017–18.

**Ae/ME 218. Statistical Mechanics. 9 units (***3-0-6); second term. Prerequisites: Ae/ME118, or equivalent. *Overview of probability and statistics, and the Maxwell-Boltzmann distribution. Overview and elements of Quantum Mechanics, degenerate energy states, particles in a box, and energy-state phase space. Statistics of indistinguishable elementary particles, Fermi-Dirac and Bose-Einstein statistics, partition functions, connections with classical thermodynamics, and the Law of Equipartition. Examples from equilibrium in fluids, solid-state physics, and others. Not offered 2017–18.

**Ae 220. Theory of Structures. ***9 units (3-0-6); first term. Prerequisite: Ae/ AM/CE/ME 102 abc. *Fundamentals of buckling and stability, total potential energy and direct equilibrium approaches; classification of instabilities into snap-through type and bifurcation type; rigid-elastic structures, eigenvalues, and eigenvectors of stiffness matrix; elastic structures; approximate estimates of buckling load; Rayleigh quotient; lateral buckling of columns: Euler strut, imperfections, Southwell plot, beam-columns, stability coefficients, buckling of frames; elasto-plastic buckling: tangent-modulus, double-modulus, Shanley’s analysis; lateral-torsional buckling of beams; buckling of plates; buckling of cylindrical shells. Not offered 2017–18.

**Ae/CE 221. Space Structures. ***9 units (3-0-6); first term. *This course examines the links between form, geometric shape, and structural performance. It deals with different ways of breaking up a continuum, and how this affects global structural properties; structural concepts and preliminary design methods that are used in tension structures and deployable structures.

Geometric foundations, polyhedra and tessellations, surfaces; space frames, examples of space frames, stiffness and structural efficiency of frames with different repeating units; sandwich plates; cable and membrane structures, form-finding, wrinkle-free pneumatic domes, balloons, tension-stabilized struts, tensegrity domes; deployable and adaptive structures, coiled rods and their applications, flexible shells, membranes, structural mechanisms, actuators, concepts for adaptive trusses and manipulators. Not offered 2017–18.

**Ae/AM/ME 223. Plasticity. ***9 units (3-0-6); third term. Prerequisite: Ae/ AM/CE/ME 102 abc or instructor’s permission. *Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stress-strain relations. Variational principles for incremental elastic-plastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and rate-sensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Not offered 2017–18.

**Ae/AM/ME/Ge 225. Special Topics in Solid Mechanics. ***Units to be arranged; first, second, third terms. *Subject matter changes depending on staff and student interest. Instructor: Rosakis.

**Ae 228. Computational Mechanics Simulations Using Particles. ***9 units (3-0-6); second term. Prerequisites: Ae/AM/CE/ME 214 or equivalent or Ae/ ACM/ME 232 or equivalent, ACM 104, ACM 105, or equivalent.Particle* simulations of continuum and discrete systems. Advances in molecular, mesoscopic, and macroscale simulations using particles, identification of common computing paradigms and challenges across disciplines, discretizations and representations using particles, fast summation algorithms, time integrators, constraints, and multiresolution. Exercises will draw on problems simulated using particles from diverse areas such as fluid and solid mechanics, computer graphics, and nanotechnology. Not offered 2017–18.

**Ae/ACM/ME 232 ab. Computational Fluid Dynamics. ***9 units (3-0-6); first, third terms. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent; ACM 100 abc or equivalent. *Development and analysis of algorithms used in the solution of fluid mechanics problems. Numerical analysis of discretization schemes for partial differential equations including interpolation, integration, spatial discretization, systems of ordinary differential equations; stability, accuracy, aliasing, Gibbs and Runge phenomena, numerical dissipation and dispersion; boundary conditions. Survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible Euler and Navier-Stokes equations, including shock-capturing methods. Not offered 2017–18

**Ae 233. Hydrodynamic Stability. ***9 units (3-0-6); second term. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent. *Laminar-stability theory as a guide to laminar-turbulent transition. Rayleigh equation, instability criteria, and response to small inviscid disturbances. Discussion of Kelvin-Helmholtz, Rayleigh-Taylor, Richtmyer-Meshkov, and other instabilities, for example, in geophysical flows. The Orr-Sommerfeld equation, the dual role of viscosity, and boundary-layer stability. Modern concepts such as pseudomomentum conservation laws and nonlinear stability theorems for 2-D and geophysical flows. Weakly nonlinear stability theory and phenomenological theories of turbulence. Not offered 2017–18.

**Ae 234 ab. Hypersonic Aerodynamics. ***9 units (3-0-6); second, third terms. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent, AM 125 abc, or instructor’s permission. *An advanced course dealing with aerodynamic problems of flight at hyper-sonic speeds. Topics are selected from hypersonic small-disturbance theory, blunt-body theory, boundary layers and shock waves in real gases, heat and mass transfer, testing facilities and experiment. Instructor: Austin.

**Ae 235. Rarefied Gasdynamics. ***9 units (3-0-6); first term. *Molecular description of matter; distribution functions; discrete-velocity gases. Kinetic theory: free-path theory, internal degrees of freedom. Boltzmann equation: BBGKY hierarchy and closure, H theorem, Euler equations, Chapman-Enskog procedure, free-molecule flows. Collisionless and transitional flows. Direct simulation Monte Carlo methods. Applications. Instructor: Pullin.

**Ae 237 ab. Nonsteady Gasdynamics. ***9 units (3-0-6); first term. *Part a: dynamics of shock waves, expansion waves, and related discontinuities in gases. Adiabatic phase-transformation waves. Interaction of waves in oneand two-dimensional flows. Boundary layers and shock structure. Applications and shock tube techniques. Part b: shock and detonation waves in solids and liquids. Equations of state for hydrodynamic computations in solids, liquids, and explosive reaction products. CJ and ZND models of detonation in solids and liquids. Propagation of shock waves and initiation of reaction in explosives. Interactions of detonation waves with water and metals. Instructor: Not offered 2017–18.

**Ae 239 ab. Turbulence. ***9 units (3-0-6); second, third terms. Prerequisites: Ae/APh/CE/ME 101 abc; AM 125 abc or ACM 101. *Reynolds-averaged equations and the problem of closure. Statistical description of turbulence. Homogeneous isotropic turbulence and structure of fine scales. Turbulent shear flows. Physical and spectral models. Subgridscale modeling. Turbulent mixing. Structure of low and high Reynolds number wall turbulence. Instructor: Dimotakis.

**Ae 240. Special Topics in Fluid Mechanics. ***Units to be arranged; first, second, third terms. *Subject matter changes depending upon staff and student interest. (1) Educational exchange at Ecole Polytechnique. Students participating in the Ecole Polytechnique educational exchange must register for 36 units while they are on detached duty at Ecole Polytechnique. For further information refer to the graduate option information for Aerospace. Instructor: Meiron.

**Ae 241. Special Topics in Experimental Fluid and Solid Mechanics. ***Prerequisite: Ae/APh 104 or equivalent or instructor’s permission. Units to be arranged; first, second, third terms. Subject matter changes depending upon staff and student interest*. Instructor: Willert.

**Ae/BE 242. Biological Flows: Propulsion. ***9 units (3-0-6); third term. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent or ChE 103 a. *Physical principles of unsteady fluid momentum transport: equations of motion, dimensional analysis, conservation laws. Unsteady vortex dynamics: vorticity generation and dynamics, vortex dipoles/rings, wake structure in unsteady flows. Life in moving fluids: unsteady drag, added-mass effects, virtual buoyancy, bounding and schooling, wake capture. Thrust generation by flapping, undulating, rowing, jetting. Low Reynolds number propulsion. Bioinspired design of propulsion devices. Not offered 2017–18.

**MedE/BE/Ae 243. Biological Flows: Transport and Circulatory Systems. ***9 units (3-0-6); second term. For course description, see Medical Engineering*.

**Ae 244. Mechanics of Nanomaterials. ***9 units (3-0-6); second term. *Basics of the mechanics of nanomaterials, including the physical and chemical synthesis/processing techniques for creating nanostructures and their relation with mechanical and other structural properties. Overview of the properties of various types of nanomaterials including nanostructured metals/ceramics/composites, nanowires, carbon nanotubes, quantum dots, nanopatterns, self-assembled colloidal crystals, magnetic nanomaterials, and biorelated nanomaterials. Innovative experimental methods and micro-structural characterization developed for studying the mechanics at the nanoscale will be described. Recent advances in the application of nanomaterials in engineering systems and patent-related aspects of nanomaterials will also be covered. Open to undergraduates with instructor’s permission. Not offered 2017–18.

**Ae 250. Reading and Independent Study. ***Units to be arranged; first, second, third terms. *Graded pass/fail only.

**Ae/CDS/ME 251 ab. Closed Loop Flow Control. ***9 units; (3-0-6 a, **1-6-1 b); second, third term. Prerequisites: ACM 100abc, Ae/APh/CE/ME 101abc or equivalent. *This course seeks to introduce students to recent developments in theoretical and practical aspects of applying control to flow phenomena and fluid systems. Lecture topics in the second term drawn from: the objectives of flow control; a review of relevant concepts from classical and modern control theory; high-fidelity and reduced-order modeling; principles and design of actuators and sensors. Third term: laboratory work in open- and closed-loop control of boundary layers, turbulence, aerodynamic forces, bluff body drag, combustion oscillations and flow-acoustic oscillations. Not offered 2017–18.

**ME/Ge/Ae 266 ab. Dynamic Fracture and Frictional Faulting. ***9 units (3-0-6)***. **For course description, see Mechanical Engineering.