Online courses directory (273)

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.

We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion.

Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.

This course describes the processes by which mass, momentum, and energy are transported in plasmas, with special reference to magnetic confinement fusion applications.

The Fokker-Planck collision operator and its limiting forms, as well as collisional relaxation and equilibrium, are considered in detail. Special applications include a Lorentz gas, Brownian motion, alpha particles, and runaway electrons.

The Braginskii formulation of classical collisional transport in general geometry based on the Fokker-Planck equation is presented.

Neoclassical transport in tokamaks, which is sensitive to the details of the magnetic geometry, is considered in the high (Pfirsch-Schluter), low (banana) and intermediate (plateau) regimes of collisionality.

This course provides an introduction to nuclear science and its engineering applications. It describes basic nuclear models, radioactivity, nuclear reactions and kinematics; covers the interaction of ionizing radiation with matter, with an emphasis on radiation detection, radiation shielding, and radiation effects on human health; and presents energy systems based on fission and fusion nuclear reactions, as well as industrial and medical applications of nuclear science.

This course covers the fundamentals of Newtonian mechanics, including kinematics, motion relative to accelerated reference frames, work and energy, impulse and momentum, 2D and 3D rigid body dynamics. The course pays special attention to applications in aerospace engineering including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. By the end of the semester, students should be able to construct idealized (particle and rigid body) dynamical models and predict model response to applied forces using Newtonian mechanics.

This is the second course in a two-semester sequence on astrophysics. Topics include galactic dynamics, groups and clusters on galaxies, phenomenological cosmology, Newtonian cosmology, Roberston-Walker models, and galaxy formation.

This course is offered for graduate students who are interested in the interdisciplinary study of bio-inspired structures. The intent is to introduce students to newly inspired modern advanced structures and their applications. It aims to link traditional advanced composites to bio-inspired structures and to discuss their generic properties. A link between materials design, strength and structural behavior at different levels (material, element, structural and system levels) is made. For each level, various concepts will be introduced. The importance of structural, dynamic, thermodynamic and kinetic theories related to such processing is highlighted. The pedagogy is based on active learning and a balance of guest lectures and hands-on activities.

This course focuses on the practical applications of the continuum concept for deformation of solids and fluids, emphasizing force balance. Topics include stress tensor, infinitesimal and finite strain, and rotation tensors. Constitutive relations applicable to geological materials, including elastic, viscous, brittle, and plastic deformation are studied.

This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.

Acknowledgements

This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching, Class of '72 Fund for Educational Innovation). The instructors gratefully acknowledge the financial support. The course was approved by the Undergraduate Committee of the MIT Department of Aeronautics and Astronautics in 2003. The instructors thank Prof. Manuel Martinez-Sanchez and the committee members for their support and suggestions.

Applies solid mechanics to analysis of high-technology structures. Structural design considerations. Review of three-dimensional elasticity theory; stress, strain, anisotropic materials, and heating effects. Two-dimensional plane stress and plane strain problems. Torsion theory for arbitrary sections. Bending of unsymmetrical section and mixed material beams. Bending, shear, and torsion of thin-wall shell beams. Buckling of columns and stability phenomena. Introduction to structural dynamics. Exercises in the design of general and aerospace structures.

This course covers interpretations of the concept of probability. Topics include basic probability rules; random variables and distribution functions; functions of random variables; and applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. The course also considers elements of statistics; Bayesian methods in engineering; methods for reliability and risk assessment of complex systems (event-tree and fault-tree analysis, common-cause failures, human reliability models); uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling); and an introduction to Markov models. Examples and applications are drawn from nuclear and other industries, waste repositories, and mechanical systems.

This course explores the theory of self-assembly in surfactant-water (micellar) and surfactant-water-oil (micro-emulsion) systems. It also introduces the theory of polymer solutions, as well as scattering techniques, light, x-ray, and neutron scattering applied to studies of the structure and dynamics of complex liquids, and modern theory of the liquid state relevant to structured (supramolecular) liquids.

This class includes a brief review of applied aerodynamics and modern approaches in aircraft stability and control. Topics covered include static stability and trim; stability derivatives and characteristic longitudinal and lateral-directional motions; and physical effects of the wing, fuselage, and tail on aircraft motion. Control methods and systems are discussed, with emphasis on flight vehicle stabilization by classical and modern control techniques; time and frequency domain analysis of control system performance; and human-pilot models and pilot-in-the-loop controls with applications. Other topics covered include V/STOL stability, dynamics, and control during transition from hover to forward flight; parameter sensitivity; and handling quality analysis of aircraft through variable flight conditions. There will be a brief discussion of motion at high angles-of-attack, roll coupling, and other nonlinear flight regimes.

Matter exists in four states - solid, liquid, gas and plasma and it will change state depending on the temperature and pressure applied to the matter. In this free online chemistry course about states of matter you will learn about the characteristics of each of the four states and the amount of energy that can be added to or taken from a substance before it starts to change state. As all substances change state at different temperatures and pressures you will learn how to use phase change diagrams to plot the energy and pressure levels, the triple point, critical temperature, boiling and melting points associated with different substances. You will also learn in a step by step manner how to calculate the change in energy needed to move a substance along the state of matter spectrum. This free online chemistry course will be of great interest to all students who wish to pursue a career in any of the sciences such as chemistry, physics, biology or geology, or the individual learner who simply wants to learn and understand what is happening when matter changes from solid to liquid to gas.<br />

Space Systems Engineering (16.83X) is the astronautical capstone course option in the Department of Aeronautics and Astronautics.  Between Spring 2002 and Spring 2003, the course was offered in a 3-semester format, using a Conceive, Design, Implement and Operate (C-D-I-O) teaching model. 16.83X is shorthand for the three course numbers: 16.83, 16.831, and 16.832. The first semester (16.83) is the Conceive-Design phase of the project, which results in a detailed system design, but precedes assembly.  The second semester (16.831) is the Implement phase, and involves building the students' system.  The final semester (16.832) is the Operate phase, in which the system is tested and readied to perform in its intended environment.

This year's project objective was to demonstrate the feasibility of an electromagnetically controlled array of formation flying satellites.  The project, "EMFFORCE", was an extension of the first C-D-I-O course project, "SPHERES", which ran from Spring 1999 through Spring 2000, and demonstrated satellite formation flying using gas thrusters for station-keeping.  The whole class works on the same project, but divides into smaller subsystem teams, such as power, metrology, and structures, to handle design details.

Gravity is the force that keeps us on the ground and understanding how gravity works is very important as it has a great influence on the upward and downward movement of objects. This free online course about gravity will explain Newton’s Second Law of Motion, the universal constant, which is used to work out the force of gravity throughout the universe. You will also learn what the effect of the earth's force of gravity, or little g as it is known, has on an object and why mass is not the same as weight. To fully understand gravity this course will take you step-by-step through the relevant formulas, showing you how to calculate velocity or distance based on time and then plot these changes so you will have a visual concept of what is happening. This course will be of great interest to students who are studying physics, chemistry, engineering, mathematics, and to students who wish to pursue a career in any of the sciences or engineering fields.<br />

This class focuses on chemical rocket propulsion systems for launch, orbital, and interplanetary flight. It studies the modeling of solid, liquid-bipropellant, and hybrid rocket engines. Thermochemistry, prediction of specific impulse, and nozzle flows including real gas and kinetic effects will also be covered. Other topics to be covered include structural constraints, propellant feed systems, turbopumps, and combustion processes in solid, liquid, and hybrid rockets.

This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus' atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.

This course uses lectures and discussion to introduce the range of topics relevant to plasma physics and fusion engineering. An introductory discussion of the economic and ecological motivation for the development of fusion power is also presented. Contemporary magnetic confinement schemes, theoretical questions, and engineering considerations are presented by expert guest lecturers. Students enrolled in the course also tour the Plasma Science and Fusion Center experimental facilities.

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.

Satellite Engineering introduces students to subsystem design in engineering spacecraft. The course presents characteristic subsystems, such as power, structure, communication and control, and analyzes the engineering trades necessary to integrate subsystems successfully into a satellite. Discussions of spacecraft operating environment and orbital mechanics help students to understand the functional requirements and key design parameters for satellite systems.