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Course 2: Mechanical Engineering |
 | | | 2.000-2.199 | | | 2.20-2.7999 | | | 2.80-2.999 plus Thesis, UROP, UPOP | | |  |
Freshman Year Introductory Subjects2.00A[J] Fundamentals of Engineering Design: Explore Space, Sea and Earth
 ( )Not offered regularly; consult department (Same subject as 16.00A[J]) Prereq: Physics I (GIR), Calculus I (GIR) Units: 3-3-3 
Student teams formulate and complete space/earth/ocean exploration-based design projects with weekly milestones. Introduces core engineering themes, principles, and modes of thinking. Specialized learning modules enable teams to focus on the knowledge required to complete their projects, such as machine elements, electronics, design process, visualization and communication. Includes exercises in written and oral communication and team building. Examples of projects include surveying a lake for millfoil, from a remote controlled aircraft, and then sending out robotic harvesters to clear the invasive growth; and exploration to search for the evidence of life on a moon of Jupiter, with scientists participating through teleoperation and supervisory control of robots. Enrollment limited; preference to freshmen. A. H. Techet, D. Newman 2.00B Toy Product Design
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Prereq: None Units: 3-5-1
Provides students with an overview of design for entertainment and play, as well as opportunities in creative product design and community service. Students develop ideas for new toys that serve clients in the community, and work in teams with local sponsors and with experienced mentors on a themed toy design project. Students enhance creativity and experience fundamental aspects of the product development process, including determining customer needs, brainstorming, estimation, sketching, sketch modeling, concept development, design aesthetics, detailed design, and prototyping. Includes written, visual, and oral communication. Enrollment limited; preference to freshmen. D. R. Wallace Core Undergraduate Subjects2.00 Introduction to Design
( ); second half of term
Prereq: None Units: 2-2-2  Begins Oct 24. Lecture: MW3.30-5 (3-370) Lab: R2-5 (35-307) or F9.30-12.30 (35-307) or F2-5 (35-307)
Project-based introduction to product development and engineering design. Emphasizes key elements of the design process, including defining design problems, generating ideas, and building solutions. Presents a range of design techniques to help students think about, evaluate, and communicate designs, from sketching to physical prototyping, as well as other types of modeling. Students work both individually and in teams. Enrollment limited; preference to Course 2-A sophomores. M. Yang No textbook information available 2.001 Mechanics and Materials I
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Prereq: Physics I (GIR); Coreq: 18.03 or 2.087 Units: 3-2-7 Lecture: TR11-12.30 (10-250) Lab: TBA Recitation: M9.30-11 (5-134) or M11-12.30 (5-217) or M2-3.30 (5-134) or M3.30-5 (5-217) or T1-2.30 (5-233) or T2.30-4 (5-233) or T EVE (7-8.30 PM) (5-233) +final
Introduction to statics and the mechanics of deformable solids. Emphasis on the three basic principles of equilibrium, geometric compatibility, and material behavior. Stress and its relation to force and moment; strain and its relation to displacement; linear elasticity with thermal expansion. Failure modes. Application to simple engineering structures such as rods, shafts, beams, and trusses. Application to biomechanics of natural materials and structures. G. Barbastathis, A. E. Hosoi, K. Kamrin No textbook information available 2.002 Mechanics and Materials II
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Prereq: 2.001, or 2.01 and 2.02B; Chemistry (GIR) Units: 3-3-6
Introduces mechanical behavior of engineering materials, and the use of materials in mechanical design. Emphasizes the fundamentals of mechanical behavior of materials, as well as design with materials. Major topics: elasticity, plasticity, limit analysis, fatigue, fracture, and creep. Materials selection. Laboratory experiments involving projects related to materials in mechanical design. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. L. Anand, K. Kamrin, P. Reis 2.003[J] Dynamics and Control I
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(Same subject as 1.053[J]) Prereq: Physics II; Coreq: 18.03 or 2.087 Units: 4-1-7 Lecture: TR9.30-11 (10-250) Recitation: R12 (5-233) or R1 (5-233) or R3 (5-233) or R4 (5-233) or F2 (1-246) or F3 (1-246) +final
Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. J. K. Vandiver, N. C. Makris, N. M. Patrikalakis, T. Peacock, D. Gossard, K. Turitsyn No textbook information available 2.004 Dynamics and Control II
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Prereq: 2.003 or 2.03; Physics II (GIR) Units: 4-2-6 Lecture: TR9.30-11,F11 (3-270) Lab: M1-3 (3-062) or M3-5 (3-062) or T1-3 (3-062) or T3-5 (3-062) +final
Modeling, analysis, and control of dynamic systems. System modeling: lumped parameter models of mechanical, electrical, and electromechanical systems; interconnection laws; actuators and sensors. Linear systems theory: linear algebra; Laplace transform; transfer functions, time response and frequency response, poles and zeros; block diagrams; solutions via analytical and numerical techniques; stability. Introduction to feedback control: closed-loop response; PID compensation; steady-state characteristics, root-locus design concepts, frequency-domain design concepts. Laboratory experiments and control design projects. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. G. Barbastathis, D. Del Vecchio, D. C. Gossard, D. E. Hardt, S. Lloyd No textbook information available 2.005 Thermal-Fluids Engineering I
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Prereq: Physics II (GIR), Calculus II (GIR); 2.086, 6.0002, or 18.06; or permission of instructor Units: 5-0-7 Lecture: MW9-11 (1-190) Recitation: F11 (1-371) or F12 (1-371) or F1 (1-371) +final
Integrated development of the fundamental principles of thermodynamics, fluid mechanics, and heat transfer with applications. Focuses on the development of the first and second laws of thermodynamics with special consideration of the rate processes associated with heat transfer and work transfer. Entropy generation and its influence on the performance of engineering systems. Conduction heat transfer in solids including steady-state and transient situations. Finned surfaces. Coupled and uncoupled fluid models. Hydrostatics. Inviscid flow analysis and Bernoulli equation. Internal and external laminar viscous flows. Turbulence. Boundary layers. Head loss in pipes. J. G. Brisson, J. Buongiorno, P. F. J. Lermusiaux, K. Varanasi Textbooks (Fall 2016) 2.006 Thermal-Fluids Engineering II
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Prereq: 2.005; or 2.051, 2.06 Units: 5-0-7 Lecture: MW9.30-11,F9 (3-370) Recitation: F11 (1-242) or F1 (1-242) or F2 (1-242) +final
Focuses on the application of the principles of thermodynamics, heat transfer, and fluid mechanics to the design and analysis of engineering systems. Laminar and turbulent flow. Heat transfer associated with laminar and turbulent flow of fluids in free and forced convection in channels and over surfaces. Pure substance model. Heat transfer in boiling and condensation. Thermodynamics and fluid mechanics of steady flow components of thermodynamic plants. Heat exchanger design. Power cycles and refrigeration plants. Design of thermodynamic plants. Radiation heat transfer. Multi-mode heat transfer and fluid flow in thermodynamic plants. J. G. Brisson, A. E. Hosoi, R. Karnik, G. H. McKinley Textbooks (Fall 2016) 2.007 Design and Manufacturing I
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Prereq: 2.001 or 2.01; 2.670; Coreq: 2.086 Units: 3-4-5
Develops students' competence and self-confidence as design engineers. Emphasis on the creative design process bolstered by application of physical laws. Instruction on how to complete projects on schedule and within budget. Robustness and manufacturability are emphasized. Subject relies on active learning via a major design-and-build project. Lecture topics include idea generation, estimation, concept selection, visual thinking, computer-aided design (CAD), mechanism design, machine elements, basic electronics, technical communication, and ethics. Lab fee. Limited enrollment. Pre-registration required for lab assignment; special sections by lottery only. D. Frey, S. Kim, A. Winter 2.008 Design and Manufacturing II
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Prereq: 2.007 or Coreq: 2.017; 2.005 or 2.051 Units: 3-3-6 Lecture: MW11-12.30 (4-370) Lab: M2-5 (35-520) or T9-12 (35-308) or T2-5 (35-308) or W2-5 (35-520) or R9-12 (35-308) or R2-5 (35-308)
Integration of design, engineering, and management disciplines and practices for analysis and design of manufacturing enterprises. Emphasis is on the physics and stochastic nature of manufacturing processes and systems, and their effects on quality, rate, cost, and flexibility. Topics include process physics and control, design for manufacturing, and manufacturing systems. Group project requires design and fabrication of parts using mass-production and assembly methods to produce a product in quantity. Six units may be applied to the General Institute Lab Requirement. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. J.-H. Chun, M. L. Culpepper, S. Kim, S. G. Kim, S. E. Sarma, J. Hart No textbook information available 2.009 The Product Engineering Process
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Prereq: 2.001 or 2.01; 2.003 or 2.03; 2.005 or 2.051; 2.670, 2.678 or 2.00B Units: 3-3-6 URL: http://web.mit.edu/2.009/www/ Lecture: MWF1 (10-250) Lab: T2-5 (3-037A) or T2-5 (3-037B) or T EVE (7-10 PM) (3-037A) or T EVE (7-10 PM) (3-037B) or T EVE (7-10 PM) (3-037C) or T EVE (7-10 PM) (3-037D) or W2-5 (3-037A) or W2-5 (3-037B) or W2-5 (3-037C) or W2-5 (3-037D) or W EVE (7-10 PM) (3-037A) or W EVE (7-10 PM) (3-037B) or R9-12 (3-037A) or R9-12 (3-037B) or R2-5 (3-037A) or R2-5 (3-037B)
Students develop an understanding of product development phases and experience working in teams to design and construct high-quality product prototypes. Design process learned is placed into a broader development context. Primary goals are to improve ability to reason about design alternatives and apply modeling techniques appropriate for different development phases; understand how to gather and process customer information and transform it into engineering specifications; and use teamwork to resolve the challenges in designing and building a substantive product prototype. Instruction and practice in oral communication provided. Enrollment may be limited due to laboratory capacity; preference to Course 2 seniors. D. R. Wallace No textbook information available 2.013 Engineering Systems Design
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Prereq: 2.001 or 2.01; 2.003 or 2.03; 2.005 or 2.051; 2.670, 2.678 or 2.00B Units: 0-6-6 Lecture: TR2.30-5 (NE45-202)
Focuses on the design of engineering systems to satisfy stated performance, stability, and/or control requirements. Emphasizes individual initiative, application of fundamental principles, and the compromises inherent in the engineering design process. Culminates in the design of an engineering system, typically a vehicle or other complex system. Includes instruction and practice in written and oral communication through team presentations, design reviews, and written reports. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. D. Hart No required or recommended textbooks 2.014 Engineering Systems Development
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Prereq: 2.001 or 2.01; 2.003 or 2.03; 2.005 or 2.051; 2.670, 2.678 or 2.00B Units: 0-6-6
Focuses on implementation and operation of engineering systems. Emphasizes system integration and performance verification using methods of experimental inquiry. Students refine their subsystem designs and the fabrication of working prototypes. Includes experimental analysis of subsystem performance and comparison with physical models of performance and with design goals. Component integration into the full system, with detailed analysis and operation of the complete vehicle in the laboratory and in-the-field. Includes written and oral reports. Students carry out formal reviews of the overall system design. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. D. Hart 2.016 Hydrodynamics
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Prereq: 2.01 or 2.001 Units: 4-2-6 Lecture: TR11-12.30 (3-442) Recitation: T3 (5-134) or W4 (5-134)
Principles of conservation of mass, momentum and energy in fluid mechanics. Basic geophysical fluid mechanics, including the effects of salinity, temperature, and density; heat balance in the ocean; large scale flows. Hydrostatics. Linear free surface waves, wave forces on floating and submerged structures. Added mass, lift and drag forces. Introduction to ocean acoustics; sound propagation and refraction. Sonar equation. Laboratory sessions in wave propagation, lift and drag forces on submerged bodies, and sound propagation. Meets with 2.06 first half of term. A. H. Techet, P. D. Sclavounos No textbook information available 2.017[J] Design of Electromechanical Robotic Systems
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(Same subject as 1.015[J]) Prereq: 2.003 or 2.03; Coreq: 2.005, 2.05 and 2.051, or 2.016; 2.671 Units: 3-3-6
Design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Basic statistics, linear systems, Fourier transforms, random processes, spectra and extreme events with applications in design. Lectures on ethics in engineering practice included. Enrollment may be limited due to laboratory capacity. F. S. Hover, J. J. Leonard 2.019 Design of Ocean Systems
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Prereq: 2.001; 2.003; 2.005 or 2.016 Units: 3-3-6
Complete cycle of designing an ocean system using computational design tools for the conceptual and preliminary design stages. Team projects assigned, with each student responsible for a specific subsystem. Lectures cover hydrodynamics; structures; power and thermal aspects of ocean vehicles, environment, materials, and construction for ocean use; generation and evaluation of design alternatives. Focus on innovative design concepts chosen from high-speed ships, submersibles, autonomous vehicles, and floating and submerged deep-water offshore platforms. Lectures on ethics in engineering practice included. Instruction and practice in oral and written communication provided. Enrollment may be limited due to laboratory capacity; preference to Course 2 seniors. C. Chryssostomidis, M. S. Triantafyllou 2.02A Engineering Materials: Properties and Applications
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Prereq: 2.01 Units: 2-0-4 Ends Oct 21. Lecture: TR11-12.30 (3-333) Recitation: T2-3.30 (5-217) or T3.30-5 (5-217) or W2-3.30 (5-234) +final
Introduction to the physical mechanisms that give rise to mechanical properties of engineering materials: stiffness, creep, stress-relaxation, strength, fracture-toughness, and fatigue. Also covers materials selection for mechanical design. Includes case studies on materials-limited problems in engineering design. A. Kolpak No textbook information available 2.03 Dynamics I
(, ); first half of term
Prereq: Physics II; Coreq: 18.03 or 2.087 Units: 2-0-4 Ends Oct 21. Lecture: TR9.30-11 (10-250) Recitation: R12 (5-233) or R1 (5-233) or R3 (5-233) or R4 (5-233) or F2 (1-246) or F3 (1-246)
Introduction to the dynamics of one and two degree-of-freedom mechanical systems. Kinematics. Force-momentum formulation for particles and rigid bodies. Work-energy concepts. Rotation of rigid bodies, angular momentum, torques and moments of inertia. Newton, Euler equations (direct method in dynamics). Conservation laws in dynamics. Basics of equilibrium, linearization and stability analysis. Includes MATLAB modeling of dynamical systems with applications. Meets with 2.003 first half of term. D. Gossard, K. Turitsyn, T. Peacock No textbook information available 2.031 Dynamics II
(, ); second half of term
Prereq: 2.03 Units: 2-0-4 Begins Oct 24. Lecture: TR9.30-11 (10-250) Recitation: R12 (5-233) or R1 (5-233) or R3 (5-233) or R4 (5-233) or F2 (1-246) or F3 (1-246) +final
Continuation of topics introduced in 2.03, including work-energy concepts, Lagrange's equations for systems of particles and rigid bodies in planar motion, and matrix eigenvalue problems. Meets with 2.003 second half of term. D. Gossard, K. Turitsyn, T. Peacock No textbook information available 2.04A Systems and Controls
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Prereq: None. Coreq: 2.03 Units: 2-1-3
Introduction to linear systems, transfer functions, and Laplace transforms. Covers stability and feedback, and provides basic design tools for specifications of transient response. Briefly covers frequency-domain techniques. Enrollment may be limited due to laboratory capacity. G. Barbastathis 2.04B Introduction to Mechanical Vibration
 (); second half of term
Prereq: 2.03, 2.086 Units: 2-1-3
Analyzes the time domain response of single- and multiple-degree-of-freedom (DOF) systems to initial conditions and force inputs. Uses matrix formulation of multiple-DOF problems, including finding natural frequencies and mode shapes. Provides an introduction to the method of normal mode superposition. Includes transfer function analysis of the response of linear systems to steady state harmonic inputs, with application to vibration isolation and dynamic absorbers. Also includes application to the analysis of machines with rotating imbalances. Enrollment may be limited due to lab capacity; preference to Course 2 majors and minors. J. K. Vandiver 2.05 Thermodynamics
(); first half of term
Prereq: 2.01 or 2.001 Units: 3-0-3 Ends Oct 21. Lecture: MW9.30-11 (3-270) Recitation: M1-2.30 (3-442) or M2.30-4 (3-442) or W1-2.30 (3-442) or W2.30-4 (3-442)
Provides an introduction to thermodynamics, including first law (coupled and uncoupled systems, incompressible liquid, ideal gas) and second law (equilibrium, reversibility and irreversibility). Explores systems in communication with heat reservoirs; quasi-static processes; and heat engines and refrigeration. Properties of open systems, including mass, energy and entropy transfer. C. Buie No textbook information available 2.051 Introduction to Heat Transfer
(); second half of term
Prereq: 2.05 Units: 2-0-4 Begins Oct 24. Lecture: MW9.30-11 (3-270) +final
Introduces fundamental processes of heat transfer. Fourier's law. Heat conduction processes including thermal resistance, lumped capacitance, fins, and the heat equation. Elementary convection, including laminar and turbulent boundary layers, internal flow, and natural convection. Thermal radiation, including Stefan-Boltzmann law, small object in large enclosure, and parallel plates. Basic concepts of heat exchangers. J. H. Lienhard, E. N. Wang, A. Hosoi No required or recommended textbooks 2.06 Fluid Dynamics
(, ); first half of term
Prereq: 2.01 or 2.001 Units: 2-0-4 Ends Oct 21. Lecture: TR11-12.30 (3-442) Recitation: T3 (5-134) or W4 (5-134)
Introduction to principal concepts and methods of fluid mechanics. Pressure, hydrostatics, and buoyancy. Control volume analysis. Mass conservation and momentum conservation for moving fluids. Viscous fluid flows, flow through pipes. Dimensional analysis. Boundary layers, and lift and drag on objects. Meets with 2.016 first half of fall term. Also offered second half of spring term. G. H. McKinley, K. Varanasi, A. Techet Textbooks (Fall 2016) 2.086 Numerical Computation for Mechanical Engineers
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Prereq: Physics I (GIR), Calculus II (GIR); Coreq: 18.03 or 2.087 Units: 1-3-8 1st mtg Sep 7. Room TBA. Lecture: M1 (26-100) Lab: M9-12 (1-115) or M2-5 (1-115) or T2-5 (1-115) or W2-5 (1-115) or F10-1 (1-115) or F2-5 (1-115) +final
Covers elementary programming concepts, including variable types, data structures, and flow control. Provides an introduction to linear algebra and probability. Numerical methods relevant to MechE, including approximation (interpolation, least squares, and statistical regression), integration, solution of linear and nonlinear equations, and ordinary differential equations. Presents deterministic and probabilistic approaches. Uses examples from MechE, particularly from robotics, dynamics, and structural analysis. Assignments require MATLAB programming. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors. N. Hadjiconstantinou, A. Patera, D. Frey, A. Hosoi No textbook information available 2.087 Engineering Mathematics: Linear Algebra and ODEs
(, ); first half of term
Prereq: Calculus II (GIR), Physics I (GIR) Units: 2-0-4 Ends Oct 21. Lecture: MW9.30-11 (3-333) Recitation: M2-3.30 (5-234)
Introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Linear systems of equations, existence and uniqueness of solutions, Gaussian elimination. Initial value problems, 1st and 2nd order systems, forward and backward Euler, RK4. Eigenproblems, eigenvalues and eigenvectors, including complex numbers, functions, vectors and matrices. A. Hosoi, T. Peacock No textbook information available Dynamics and Acoustics2.032 Dynamics
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Prereq: 2.003 Units: 4-0-8 URL: http://web.mit.edu/2.032/www/ Lecture: MW1-2.30 (3-370)
Review of momentum principles. Hamilton's principle and Lagrange's equations. Three-dimensional kinematics and dynamics of rigid bodies. Study of steady motions and small deviations therefrom, gyroscopic effects, causes of instability. Free and forced vibrations of lumped-parameter and continuous systems. Nonlinear oscillations and the phase plane. Nonholonomic systems. Introduction to wave propagation in continuous systems. T. R. Akylas, T. Peacock, N. Hadjiconstantinou No textbook information available 2.034[J] Nonlinear Dynamics and Waves
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(Same subject as 1.685[J], 18.377[J]) Prereq: Permission of instructor Units: 3-0-9 URL: http://web.mit.edu/2.034/www/
A unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. Nonlinear free and forced vibrations; nonlinear resonances; self-excited oscillations; lock-in phenomena. Nonlinear dispersive and nondispersive waves; resonant wave interactions; propagation of wave pulses and nonlinear Schrodinger equation. Nonlinear long waves and breaking; theory of characteristics; the Korteweg-de Vries equation; solitons and solitary wave interactions. Stability of shear flows. Some topics and applications may vary from year to year. T. R. Akylas, R. R. Rosales 2.036[J] Nonlinear Dynamics and Chaos
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(Same subject as 18.385[J]) Prereq: 18.03 or 18.034 Units: 3-0-9 URL: http://math.mit.edu/classes/18.385 Lecture: TR11-12.30 (2-136)
Introduction to the theory of nonlinear dynamical systems with applications from science and engineering. Local and global existence of solutions, dependence on initial data and parameters. Elementary bifurcations, normal forms. Phase plane, limit cycles, relaxation oscillations, Poincare-Bendixson theory. Floquet theory. Poincare maps. Averaging. Near-equilibrium dynamics. Synchronization. Introduction to chaos. Universality. Strange attractors. Lorenz and Rossler systems. Hamiltonian dynamics and KAM theory. Uses MATLAB computing environment. R. R. Rosales No textbook information available 2.050[J] Nonlinear Dynamics: Chaos
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(Same subject as 12.006[J], 18.353[J]) Prereq: 18.03 or 18.034; Physics II (GIR) Units: 3-0-9 Lecture: TR1-2.30 (2-105) +final
Introduction to nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincare sections, fractal dimension, and Lyapunov exponents. Applications to mechanical systems, fluid dynamics, physics, geophysics, and chemistry. See 12.207J/18.354J for Nonlinear Dynamics: Continuum Systems. P-T. Brun No textbook information available 2.060[J] Structural Dynamics and Vibrations
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(Same subject as 1.581[J], 16.221[J]) (Subject meets with 1.058) Prereq: Permission of instructor Units: 3-1-8 Lecture: MWF10 (1-390) Recitation: W4 (1-246)
Single- and multiple-degree-of-freedom vibration problems, using matrix formulation and normal mode superposition methods. Time and frequency domain solution techniques including convolution and Fourier transforms. Applications to vibration isolation, damping treatment, and dynamic absorbers. Analysis of continuous systems by exact and approximate methods. Applications to buildings, ships, aircraft and offshore structures. Vibration measurement and analysis techniques. Students should possess basic knowledge in structural mechanics and in linear algebra. Students taking graduate version complete additional assignments. E. Kausel, J. K. Vandiver No textbook information available 2.062[J] Wave Propagation
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(Same subject as 1.138[J], 18.376[J]) Prereq: 2.003, 18.075 Units: 3-0-9 URL: http://math.mit.edu/classes/18.376/
Theoretical concepts and analysis of wave problems in science and engineering with examples chosen from elasticity, acoustics, geophysics, hydrodynamics, blood flow, nondestructive evaluation, and other applications. Progressive waves, group velocity and dispersion, energy density and transport. Reflection, refraction and transmission of plane waves by an interface. Mode conversion in elastic waves. Rayleigh waves. Waves due to a moving load. Scattering by a two-dimensional obstacle. Reciprocity theorems. Parabolic approximation. Waves on the sea surface. Capillary-gravity waves. Wave resistance. Radiation of surface waves. Internal waves in stratified fluids. Waves in rotating media. Waves in random media. T. R. Akylas, R. R. Rosales 2.065 Acoustics and Sensing
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(Subject meets with 2.066) Prereq: 2.003, 2.04B, 6.003, 8.03, or 16.003 Units: 3-0-9
2.066 Acoustics and Sensing
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(Subject meets with 2.065) Prereq: 2.003, 2.04B, 6.003, 8.03, 16.003, or permission of instructor Units: 3-0-9
Introduces the fundamental concepts of acoustics and sensing with waves. Provides a unified theoretical approach to the physics of image formation through scattering and wave propagation in sensing. The linear and nonlinear acoustic wave equation, sources of sound, including musical instruments. Reflection, refraction, transmission and absorption. Bearing and range estimation by sensor array processing, beamforming, matched filtering, and focusing. Diffraction, bandwidth, ambient noise and reverberation limitations. Scattering from objects, surfaces and volumes by Green's Theorem. Forward scatter, shadows, Babinet's principle, extinction and attenuation. Ray tracing and waveguides in remote sensing. Applications to acoustic, radar, seismic, thermal and optical sensing and exploration. Students taking the graduate version of the subject complete additional assignments. N. C. Makris Solid Mechanics and Materials2.071 Mechanics of Solid Materials
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Prereq: 2.002 or 2.02A Units: 4-0-8
Fundamentals of solid mechanics applied to the mechanical behavior of engineering materials. Kinematics of deformation, stress, and balance principles. Isotropic linear elasticity and isotropic linear thermal elasticity. Variational and energy methods. Linear viscoelasticity. Small-strain elastic-plastic deformation. Mechanics of large deformation; nonlinear hyperelastic material behavior. Foundations and methods of deformable-solid mechanics, including relevant applications. Provides base for further study and specialization within solid mechanics, including continuum mechanics, computational mechanics (e.g., finite-element methods), plasticity, fracture mechanics, structural mechanics, and nonlinear behavior of materials. L. Anand, D. M. Parks 2.072 Mechanics of Continuous Media
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Prereq: 2.071 Units: 3-0-9
Principles and applications of continuum mechanics. Kinematics of deformation. Thermomechanical conservation laws. Stress and strain measures. Constitutive equations including some examples of their microscopic basis. Solution of some basic problems for various materials as relevant in materials science, fluid dynamics, and structural analysis. Inherently nonlinear phenomena in continuum mechanics. Variational principles. L. Anand 2.073 Solid Mechanics: Plasticity and Inelastic Deformation
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Prereq: 2.071 Units: 3-0-9 Lecture: MW2.30-4 (1-150)
Physical basis of plastic/inelastic deformation of solids; metals, polymers, granular/rock-like materials. Continuum constitutive models for small and large deformation of elastic-(visco)plastic solids. Analytical and numerical solution of selected boundary value problems. Applications to deformation processing of metals. L. Anand, D. M. Parks No textbook information available 2.074 Solid Mechanics: Elasticity
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Prereq: 2.002, Coreq: 18.03 Units: 3-0-9 Lecture: MW11-12.30 (1-150)
Introduction to the theory and applications of elastic solids. Review strain, stress, and stress-strain law. Several of the following topics: Anisotropic material behavior. Piezoelectric materials. Effective properties of composites. Structural mechanics of beams and plates. Energy methods for structures. Two-dimensional problems. Stress concentration at cavities, concentrated loads, cracks, and dislocations. Variational methods and their applications; introduction to the finite element method. Introduction to wave propagation. R. Abeyaratne No textbook information available 2.076[J] Mechanics of Heterogeneous Materials
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(Same subject as 16.223[J]) Prereq: 2.002, 3.032, 16.20, or permission of instructor Units: 3-0-9
Mechanical behavior of heterogeneous materials such as thin-film microelectro- mechanical systems (MEMS) materials and advanced filamentary composites, with particular emphasis on laminated structural configurations. Anisotropic and crystallographic elasticity formulations. Structure, properties and mechanics of constituents such as films, substrates, active materials, fibers, and matrices including nano- and micro-scale constituents. Effective properties from constituent properties. Classical laminated plate theory for modeling structural behavior including extrinsic and intrinsic strains and stresses such as environmental effects. Introduction to buckling of plates and nonlinear (deformations) plate theory. Other issues in modeling heterogeneous materials such as fracture/failure of laminated structures. B. L. Wardle, S-G. Kim 2.080[J] Structural Mechanics
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(Same subject as 1.573[J]) Prereq: 2.002 Units: 4-0-8 Lecture: MW2.30-4 (2-105) Recitation: F9 (5-217)
Presents fundamental concepts of structural mechanics with applications to marine, civil, and mechanical structures. Covers residual stresses; thermal effects; analysis of beams, columns, tensioned beams, trusses, frames, arches, cables, and shafts of general shape and material, including composites; elastic buckling of columns; exact and approximate methods, energy methods, principle of virtual work, and introduction to computational structural mechanics. T. Wierzbicki, H. Schmidt No textbook information available 2.081[J] Plates and Shells: Static and Dynamic Analysis
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(Same subject as 16.230[J]) Prereq: 2.071, 2.080J, or Permission of Instructor Units: 3-1-8
Stress-strain relations for plate and shell elements. Differential equations of equilibrium. Energy methods and approximate solutions. Bending and buckling of rectangular plates. Post-buckling and ultimate strength of cold formed sections and typical stiffened panels used in aerospace, civil, and mechanical engineering; offshore technology; and ship building. Geometry of curved surfaces. General theory of elastic, axisymmetric shells and their equilibrium equations. Buckling, crushing and bending strength of cylindrical shells with applications. Propagation of 1-D elastic waves in rods, geometrical and material dispersion. Plane, Rayleigh surface, and 3-D waves. 1-D plastic waves. Response of plates and shells to high-intensity loads. Dynamic plasticity and fracture. Application to crashworthiness and impact loading of structures. T. Sapsis 2.082 Ship Structural Analysis and Design
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Prereq: 2.081, 2.701 Units: 3-0-3
Design application of analysis developed in 2.081J. Ship longitudinal strength and hull primary stresses. Ship structural design concepts. Design limit states including plate bending, column and panel buckling, panel ultimate strength, and plastic analysis. Matrix stiffness, and introduction to finite element analysis. Computer projects on the structural design of a midship module. R. S. McCord, T. Wierzbicki 2.084[J] Structural Mechanics in Nuclear Power Technology
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(Same subject as 1.56[J], 22.314[J]) Prereq: 2.001 or permission of instructor Units: 3-0-9
Structural components in nuclear power plant systems, their functional purposes, operating conditions, and mechanical/structural design requirements. Combines mechanics techniques with models of material behavior to determine adequacy of component design. Considerations include mechanical loading, brittle fracture, inelastic behavior, elevated temperatures, neutron irradiation, vibrations and seismic effects. Staff Computational Engineering2.089[J] Computational Geometry
()Not offered regularly; consult department (Same subject as 1.128[J]) Prereq: Permission of instructor Units: 3-0-9
Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments. N. M. Patrikalakis, D. C. Gossard 2.091[J] Software and Computation for Simulation
()Not offered regularly; consult department (Same subject as 1.124[J]) Prereq: 1.00 or permission of instructor Units: 3-0-9
Modern software development techniques and algorithms for engineering computation. Hands-on investigation of computational and software techniques for simulating engineering systems, such as sensor networks, traffic networks, and discrete simulation of materials using atomistic and particle methods. Covers data structures and algorithms for modeling, analysis, and visualization in the setting of multi-core and distributed computing. Treatment of basic topics, such as queuing, sorting and search algorithms, and more advanced numerical techniques based on state machines and distributed agents. Foundation for in-depth exploration of image processing, optimization, finite element and particle methods, computational materials, discrete element methods, and network methods. Knowledge of an object-oriented language required. J. R. Williams 2.092 Finite Element Analysis of Solids and Fluids I
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(Subject meets with 2.093) Prereq: 2.001 or 2.01; 2.003 or 2.03 Units: 3-0-9 URL: http://ocw.mit.edu/courses/mechanical-engineering/2-092-finite-element-analysis-of-solids-and-fluids-i-fall-2009/index.htm
2.093 Finite Element Analysis of Solids and Fluids I
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(Subject meets with 2.092) Prereq: 2.001 or 2.01; 2.003 or 2.03 Units: 3-0-9 URL: http://ocw.mit.edu/courses/mechanical-engineering/2-092-finite-element-analysis-of-solids-and-fluids-i-fall-2009/index.htm
Finite element methods for analysis of steady-state and transient problems in solid, structural, fluid mechanics, and heat transfer. Presents finite element methods and solution procedures for linear and nonlinear analyses using largely physical arguments. Demonstrates finite element analyses. Homework involves use of an existing general purpose finite element analysis program. Includes modeling of problems and interpretation of numerical results. Students taking graduate version complete additional assignments. K. J. Bathe 2.094 Finite Element Analysis of Solids and Fluids II
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Prereq: 2.001 Units: 3-0-9
Presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element methods and their applications to solution of general problems in solid, structural and fluid mechanics, heat and mass transfer, and multiphysics problems including fluid-structure interactions. Formulation of governing continuum mechanics equations, conservation laws, virtual work, and variational principles for finite element solutions. Discretization of governing equations using finite element methods; stability, accuracy and convergence of methods. Solution of central problems and a term project using an existing general purpose finite element analysis program. K. J. Bathe 2.096[J] Introduction to Numerical Simulation
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(Same subject as 6.336[J], 16.910[J]) Prereq: 18.03 or 18.06 Units: 3-3-6 Lecture: MW1-2.30 (32-141)
Introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical engineering, biology, and materials science. Topics include mathematical formulations (techniques for automatic assembly of mathematical problems from physics' principles); sparse, direct and iterative solution techniques for linear systems; Newton and Homotopy methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations; accelerated methods for integral equations; techniques for automatic generation of compact dynamical system models and model order reduction. L. Daniel, J. K. White No textbook information available 2.097[J] Numerical Methods for Partial Differential Equations
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(Same subject as 6.339[J], 16.920[J]) Prereq: 18.03 or 18.06 Units: 3-0-9 Lecture: MW9.30-11 (4-163)
Covers the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential and integral equations. Topics include mathematical formulations; finite difference, finite volume, finite element, and boundary element discretization methods; and direct and iterative solution techniques. The methodologies described form the foundation for computational approaches to engineering systems involving heat transfer, solid mechanics, fluid dynamics, and electromagnetics. Computer assignments requiring programming. Q. Wang, J. K. White No textbook information available 2.099[J] Computational Mechanics of Materials
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(Same subject as 16.225[J]) Prereq: Permission of instructor Units: 3-0-9 Lecture: TR2.30-4 (33-422) Recitation: T4 (33-422)
Formulation of numerical (finite element) methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered includes finite deformation elasticity and inelasticity. Numerical formulation and algorithms include variational formulation and variational constitutive updates; finite element discretization; constrained problems; time discretization and convergence analysis. Strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science are stressed throughout. Experience in either C++, C, or Fortran required. R. Radovitzky No textbook information available System Dynamics and Control2.110[J] Information, Entropy, and Computation
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(Same subject as 6.050[J]) Prereq: Physics I (GIR) Units: 3-0-6
Explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include information and computation, digital signals, codes, and compression. Biological representations of information. Logic circuits, computer architectures, and algorithmic information. Noise, probability, and error correction. The concept of entropy applied to channel capacity and to the second law of thermodynamics. Reversible and irreversible operations and the physics of computation. Quantum computation. P. Penfield, Jr., S. Lloyd 2.111[J] Quantum Computation
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(Same subject as 8.370[J], 18.435[J]) Prereq: Permission of instructor Units: 3-0-9 Lecture: TR1-2.30 (4-370) +final
Provides an introduction to the theory and practice of quantum computation. Topics covered: physics of information processing; quantum algorithms including the factoring algorithm and Grover's search algorithm; quantum error correction; quantum communication and cryptography. Knowledge of quantum mechanics helpful but not required. I. Chuang, E. Farhi, S. Lloyd, P. Shor Textbooks (Fall 2016) 2.12 Introduction to Robotics
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(Subject meets with 2.120) Prereq: 2.004, or 2.031 and 2.04A Units: 3-2-7 Lecture: MW2.30-4 (3-270) Lab: R11-1 (5-007) or R1-3 (5-007) or R3-5 (5-007) or F9-11 (5-007) or F11-1 (5-007) or F2-4 (5-007)
No textbook information available 2.120 Introduction to Robotics
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(Subject meets with 2.12) Prereq: 2.004, or 2.031 and 2.04A, or permission of instructor Units: 3-2-7 Lecture: MW2.30-4 (3-270) Lab: R11-1 (5-007) or R1-3 (5-007) or R3-5 (5-007) or F9-11 (5-007) or F11-1 (5-007) or F2-4 (5-007)
Presents the fundamentals of robot mechanisms, dynamics, and controls. Planar and spatial kinematics, differential motion, energy method for robot mechanics; mechanism design for manipulation and locomotion; multi-rigid-body dynamics; force and compliance control, balancing control, visual feedback, human-machine interface; actuators, sensors, wireless networking, and embedded software. Weekly laboratories include real-time control, vehicle navigation, arm and end-effector design, and balancing robot control. Group term project requires design and fabrication of robotic systems. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity. H. Asada, J. J. Leonard No textbook information available 2.131 Advanced Instrumentation and Measurement
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Prereq: Permission of Instructor Units: 3-6-3
Provides training in advanced instrumentation and measurement techniques. Topics include system level design, fabrication and evaluation with emphasis on systems involving concepts and technology from mechanics, optics, electronics, chemistry and biology. Simulation, modeling and design software. Use of a wide range of instruments/techniques (e.g., scanning electron microscope, dynamic signal/system analyzer, impedance analyzer, laser interferometer) and fabrication/machining methods (e.g., laser micro-machining, stereo lithography, computer controlled turning and machining centers). Theory and practice of both linear and nonlinear system identification techniques. No final exam. I. W. Hunter 2.14 Analysis and Design of Feedback Control Systems
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(Subject meets with 2.140) Prereq: 2.004, 2.04A, or 2.04B Units: 3-3-6 URL: http://me.mit.edu/2.14/
2.140 Analysis and Design of Feedback Control Systems
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(Subject meets with 2.14) Prereq: 2.004, 2.04A, 2.04B, or permission of instructor Units: 3-3-6
Develops the fundamentals of feedback control using linear transfer function system models. Analysis in time and frequency domains. Design in the s-plane (root locus) and in the frequency domain (loop shaping). Describing functions for stability of certain non-linear systems. Extension to state variable systems and multivariable control with observers. Discrete and digital hybrid systems and use of z-plane design. Extended design case studies and capstone group projects. Student taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity. D. Rowell, D. L. Trumper, K. Youcef-Toumi 2.141 Modeling and Simulation of Dynamic Systems
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Prereq: 2.151 Units: 3-0-9
Modeling multidomain engineering systems at a level of detail suitable for design and control system implementation. Network representation, state-space models; multiport energy storage and dissipation, Legendre transforms; nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms; Control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission. N. Hogan 2.151 Advanced System Dynamics and Control
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Prereq: 2.004, 18.06; or 2.087, 2.04A Units: 4-0-8 Lecture: TR1-2.30 (5-134) Recitation: W4 (3-442)
Analytical descriptions of state-determined dynamic physical systems; time and frequency domain representations; system characteristics - controllability, observability, stability; linear and nonlinear system responses. Modification of system characteristics using feedback. State observers, Kalman filters. Modeling/performance trade-offs in control system design. Basic optimization tools. Positive systems. Emphasizes applications to physical systems. J.-J. E. Slotine, K. Youcef-Toumi, N. Hogan Textbooks (Fall 2016) 2.152[J] Nonlinear Control
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(Same subject as 9.110[J]) Prereq: 2.151, 6.241, 16.31, or permission of instructor Units: 3-0-9
Introduction to nonlinear control and estimation in physical and biological systems. Nonlinear stability theory, Lyapunov analysis, Barbalat's lemma. Feedback linearization, differential flatness, internal dynamics. Sliding surfaces. Adaptive nonlinear control and estimation. Multiresolution bases, nonlinear system identification. Contraction analysis, differential stability theory. Nonlinear observers. Asynchronous distributed computation and learning. Concurrent synchronization, polyrhythms. Monotone nonlinear systems. Emphasizws application to physical systems (robots, aircraft, spacecraft, underwater vehicles, reaction-diffusion processes, machine vision, oscillators, internet), machine learning, computational neuroscience, and systems biology. Includes term projects. J.-J. E. Slotine 2.153 Adaptive Control
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Prereq: 2.151 Units: 3-0-9
Introduces the foundation of adaptive control in continuous-time and discrete-time systems. Adaptive control is the ability to self-correct a controller in the presence of parametric uncertainties using online information is its main and most compelling feature. Examples drawn from aerospace, propulsion, automotive, and energy systems will be used to elucidate the underlying concepts. A. Annaswamy 2.154 Maneuvering and Control of Surface and Underwater Vehicles
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Prereq: 2.22 Units: 3-0-9 Lecture: TR9.30-11 (1-132)
Maneuvering motions of surface and underwater vehicles. Derivation of equations of motion, hydrodynamic coefficients. Memory effects. Linear and nonlinear forms of the equations of motion. Control surfaces modeling and design. Engine, propulsor, and transmission systems modeling and simulation during maneuvering. Stability of motion. Principles of multivariable automatic control. Optimal control, Kalman filtering, loop transfer recovery. Term project: applications chosen from autopilots for surface vehicles; towing in open seas; remotely operated vehicles. M. S. Triantafyllou No textbook information available 2.160 Identification, Estimation, and Learning
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Prereq: 2.151 Units: 3-0-9
Provides a broad theoretical basis for system identification, estimation, and learning. Least squares estimation and its convergence properties, Kalman filter and extended Kalman filter, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation. H. Asada, J.-J. E. Slotine 2.165[J] Robotics
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(Same subject as 9.175[J]) Prereq: 2.151 or permission of instructor Units: 3-0-9
Dynamic analysis, design, and control of robots. Forward and inverse kinematics and dynamics of multi-input, multi-output rigid body systems. Computed torque control. Adaptive control. System identification. Force feedback, adaptive visual servoing. Task planning, teleoperation. Elements of biological planning and control. Motor primitives, entrainment, locomotion, active sensing, binding models. Term projects. J.-J. E. Slotine, H. Asada 2.166 Autonomous Vehicles
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Prereq: 6.041 or permission of instructor Units: 3-1-8
Theory and application of probabilistic techniques for autonomous mobile robotics. Topics include probabilistic state estimation and decision making for mobile robots; stochastic representations of the environment; dynamic models and sensor models for mobile robots; algorithms for mapping and localization; planning and control in the presence of uncertainty; cooperative operation of multiple mobile robots; mobile sensor networks; application to autonomous marine (underwater and floating), ground, and air vehicles. J. J. Leonard 2.167 Hands-On Marine Robotics
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Prereq: None Units arranged [P/D/F]
Direct experience in developing marine robotic systems, from conceptualization and design through manufacture and testing. The class consists of a weekly seminar with readings and discussions, and significant outside work on student projects, culminating in a written report each term. Seminar topics include tools for unmanned marine work and their history, analysis of mission requirements, conceptual design and modeling of systems, experiments and proofs of concept, and project pacing and time management. A total of up to 12 hours credit may be taken over one or two terms; seminar topics repeat yearly. F. S. Hover 2.171 Analysis and Design of Digital Control Systems
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Prereq: 2.14, 2.151, or permission of instructor Units: 3-3-6 URL: http://web.mit.edu/2.171/www/  Subject Cancelled
A comprehensive introduction to digital control system design, reinforced with hands-on laboratory experiences. Major topics include discrete-time system theory and analytical tools; design of digital control systems via approximation from continuous time; direct discrete-time design; loop-shaping design for performance and robustness; state-space design; observers and state-feedback; quantization and other nonlinear effects; implementation issues. Laboratory experiences and design projects connect theory with practice. D. L. Trumper 2.18[J] Biomolecular Feedback Systems
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(Same subject as 6.557[J]) (Subject meets with 2.180[J], 6.027[J]) Prereq: 18.03, Biology (GIR), or permission of instructor Units: 3-0-9
2.180[J] Biomolecular Feedback Systems
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(Same subject as 6.027[J]) (Subject meets with 2.18[J], 6.557[J]) Prereq: 18.03, Biology (GIR), or permission of instructor Units: 3-0-9
Comprehensive introduction to dynamics and control of biomolecular systems with emphasis on design/analysis techniques from control theory. Provides a review of biology concepts, regulation mechanisms, and models. Covers basic enabling technologies, engineering principles for designing biological functions, modular design techniques, and design limitations. Students taking graduate version complete additional assignments. D. Del Vecchio 2.183[J] Biomechanics and Neural Control of Movement
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(Same subject as 9.34[J]) (Subject meets with 2.184) Prereq: 2.004, 2.04A, or permission of instructor Units: 3-0-9
2.184 Biomechanics and Neural Control of Movement
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(Subject meets with 2.183[J], 9.34[J]) Prereq: 2.004, 2.04A, or permission of instructor Units: 3-0-9
Quantitative knowledge of human movement behavior is important in a growing number of engineering applications (medical and rehabilitation technology, athletic and military equipment, human-computer interaction, vehicle performance, etc.). Presents a quantitative, model-based description of how biomechanical and neural factors interact in human sensory-motor behavior, focusing mainly on the upper limbs. Students survey recent literature on how motor behavior is controlled, comparing biological and robotic approaches to similar tasks. Topics may include a review of relevant neural, muscular and skeletal physiology, neural feedback and "equilibrium-point" theories, co-contraction strategies, impedance control, kinematic redundancy, optimization, intermittency, contact tasks and tool use. Students taking the graduate version will complete additional assignments. N. Hogan |
| | | 2.000-2.199 | | | 2.20-2.7999 | | | 2.80-2.999 plus Thesis, UROP, UPOP | | | |
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