Research in Aerospace
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.
Fluid Mechanics
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.
Mechanics of Structures and Solids
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.
Aerospace Control Systems
Part a: Linear state space systems, including concepts of controllability/reachability and observability. State feedback and optimal control. Frequency domain tools (Bode plots, Nyquist analysis, input/output performance). Part b: Optimization-based design of control systems, including optimal control and receding horizon control. Introductory random processes and optimal estimation. Kalman filtering and nonlinear filtering methods for autonomous systems.
Experimental Methods
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.
Space Engineering
Part a: Design of space missions based on astrodynamics. Topics include conic orbits with perturbations (J2, drag, and solar radiation pressure), Lambert's Theorem, periodic orbits and ground tracks, invariant manifolds, and the variational equation with mission applications to planetary flybys, constellation, formation flying, and low energy planetary capture and landing. Part b: Introduction to spacecraft systems and subsystems, mission design, rocket mechanics, launch vehicles, and space environments; spacecraft mechanical, structural, and thermal design; communication and power systems; 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.
Computational Mechanics
Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code. Not offered 2025-26.
Spacecraft Navigation
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 2025-26.
Classical Thermodynamics
Fundamentals of Classical Thermodynamics. Basic 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, phase equilibrium, phase transitions, and thermodynamic properties of solids, liquids, and gases. Examples will be drawn from fluid dynamics, solid mechanics, energy systems, and thermal-science applications.
Combustion Fundamentals
Space Propulsion
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.
Aerospace Engineering Seminar
Speakers from campus and outside research and manufacturing organizations discuss current problems and advances in aerospace engineering. Graded pass/fail.
Fundamentals of Energy and Mass Transport in Small Scale Systems
The design of instrumentation for cooling, sensing or measurement in microsystems requires special knowledge of the evolution and propagation of thermal and concentration gradients in confined geometries, which ultimately control the degree of maximum energy and mass exchange. A significant challenge facing the microelectronics industry, for example, is mitigation of hot spots in densely packed high power chips for artificial intelligence to prevent thermal runaway. This course offers a concise treatment of the fundamentals of mass and energy transport by examining steady and unsteady diffusive and convective processes in small confined systems. Contrasts with macroscale behavior caused by the effects of small scale confinement and reduced dimensionality will be examined. Sample problems will be drawn from systems in applied physics, material science, electrical and bioengineering. Students must have working knowledge of vector calculus, ODEs, basic PDEs, and complex variables. Not offered 2025-26.
Introduction to the Physics of Remote Sensing
An overview of the physics behind space remote sensing instruments. Topics include the interaction of electromagnetic waves with natural surfaces, including scattering of microwaves, microwave and thermal emission from atmospheres and surfaces, and spectral reflection from natural surfaces and atmospheres in the near-infrared and visible regions of the spectrum. The class also discusses the design of modern space sensors and associated technology, including sensor design, new observation techniques, ongoing developments, and data interpretation. Examples of applications and instrumentation in geology, planetology, oceanography, astronomy, and atmospheric research. Part a offered spring term; Part b not offered 2025-26
Continuum Mechanics of Fluids and Solids
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.
Mechanics of Composite Materials and Structures
Advanced Research in Aerospace
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.
Advanced Fluid Mechanics
Extensions on the foundations of the mechanics of fluids. Basic concepts will be emphasized; transition from incompressible and potential flow to weakly compressible flow; acoustics and sound generation; transonic flow; fully compressible flow; flow past bodies and shock waves; small-Mach number expansion; Navier-Stokes shock structure; elements of the kinetic theory of gases; Lagrangian form of equations of motion; velocity-gradient tensor and vorticity; vortex dynamics; exact solutions; incompressible potential flow; free-streamline flows; scalar mixing. only part b offered in 2025-26
Technical Fluid Mechanics
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 2025-26.
Advanced Space Project
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. Not offered 2025-26.
GALCIT Colloquium
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.
Mechanics and Materials Aspects of Fracture
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. Not offered 2025-26
Computational Solid Mechanics
This course focuses on the analysis of elastic thin shell structures in the large deformation regime. Problems of interest include softening behavior, bifurcations, loss of stability and localization. Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. Variational principles. Finite element and isogeometric formulations for thin shells. Time integration, initial boundary value problems. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Not offered 2025-26.
Dynamic Behavior of Materials
Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state.
Statistical Mechanics
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 2025-26.
Theory of Structures
Fundamentals of buckling and stability, total potential energy and equilibrium approaches; snap-through and bifurcation instabilities; eigenvalues and eigenvectors of stiffness matrix; Rayleigh-Ritz estimates of buckling loads; buckling of rods; imperfection sensitivity; elastic-plastic buckling; buckling of plates and shells. Selected topics: localization and wrinkling of membranes and solids; stability landscapes for shells and other topics. Not offered 2025-26.
Space Structures
Plasticity
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 2025-26.
Multifunctional Materials
Multiscale view of materials and different approaches of introducing functionality; Electronic aspects and multiferroic materials; Symmetry breaking phase transformations, microstructure: shape-memory alloys, ferroelectrics, liquid crystal elastomers; Composite materials and metamaterials: multifunctional structures. Not offered 2025-26.
Special Topics in Solid Mechanics
Subject matter changes depending on staff and student interest. Not offered 2025-26.
Computational Fluid Dynamics
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.
Hydrodynamic Stability
Hypersonic Aerodynamics
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. Not offered 2025-26.
Rarefied Gasdynamics
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. Not offered 2025-26.
Nonsteady Gasdynamics
Turbulence
Reynolds number, transition from steady to unsteady, chaotic, and turbulent flow. Reynolds-averaged equations. Statistical description of turbulence. Physical and spectral models. Homogeneous isotropic turbulence, intermediate and small scales. Large-scale structure, and turbulent free and wall-bounded shear flows. Turbulent mixing.
Special Topics in Fluid Mechanics
Topics and subject matter descriptions change each year depending upon staff and student interest.
Special Topics in Experimental Fluid and Solid Mechanics
Subject matter changes depending upon staff and student interest. Not offered 2025-26.
Biological Flows: Propulsion
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 2025-26.
Physiological Mechanics
Internal flows: steady and pulsatile blood flow in compliant vessels, internal flows in organisms. Fluid dynamics of the human circulatory system: heart, veins, and arteries (microcirculation). Mass and momentum transport across membranes and endothelial layers. Fluid mechanics of the respiratory system. Renal circulation and circulatory system. Biological pumps. Low and High Reynolds number locomotion. Not offered 2025-26.
Reading and Independent Study
Graded pass/fail only.
Closed Loop Flow Control
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 2025-26.
Static and Dynamic Failure of Brittle Solids and Interfaces, from the Micro to the Mega
Fracture and Frictional Faulting
Introduction to elastodynamics and waves in solids. Fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Interaction of faulting with fluids. Applications to engineering phenomena a physics and mechanics of earthquakes. Not offered 2025-26.