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12.800 Fluid Dynamics of the Atmosphere and Ocean (MIT) 12.800 Fluid Dynamics of the Atmosphere and Ocean (MIT)

Description

This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site. This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site.

Subjects

meteorology | meteorology | climate | climate | oceanography | oceanography | Eulerian and Lagrangian kinematics | Eulerian and Lagrangian kinematics | mass | mass | momentum | momentum | energy | energy | Vorticity | Vorticity | divergence Scaling | divergence Scaling | geostrophic approximation | geostrophic approximation | Ekman layers | Ekman layers | Vortex motion | Vortex motion | fluid dynamics | fluid dynamics | atmospheric science | atmospheric science | physical oceanography | physical oceanography | ocean engineering | ocean engineering | oceans | oceans | fluid flow | fluid flow | conservation equations | conservation equations | vortex flows | vortex flows | circulation | circulation | Earth | Earth | rotation | rotation | GFD kinematics | GFD kinematics | waves | waves | Eulerian kinematics | Eulerian kinematics | Lagrangian kinematics | Lagrangian kinematics

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16.07 Dynamics (MIT) 16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.

Subjects

Curvilinear motion | Curvilinear motion | carteian coordinates | carteian coordinates | dynamics | dynamics | equations of motion | equations of motion | intrinsic coordinates | intrinsic coordinates | coordinate systems | coordinate systems | work | work | energy | energy | conservative forces | conservative forces | potential energy | potential energy | linear impulse | linear impulse | mommentum | mommentum | angular impulse | angular impulse | relative motion | relative motion | rotating axes | rotating axes | translating axes | translating axes | Newton's second law | Newton's second law | inertial forces | inertial forces | accelerometers | accelerometers | Newtonian relativity | Newtonian relativity | gravitational attraction | gravitational attraction | 2D rigid body kinematics | 2D rigid body kinematics | conservation laws for systems of particles | conservation laws for systems of particles | 2D rigid body dynamics | 2D rigid body dynamics | pendulums | pendulums | 3D rigid body kinematics | 3D rigid body kinematics | 3d rigid body dynamics | 3d rigid body dynamics | inertia tensor | inertia tensor | gyroscopic motion | gyroscopic motion | torque-free motion | torque-free motion | spin stabilization | spin stabilization | variable mass systems | variable mass systems | rocket equation | rocket equation | central foce motion | central foce motion | Keppler's laws | Keppler's laws | orbits | orbits | orbit transfer | orbit transfer | vibration | vibration | spring mass systems | spring mass systems | forced vibration | forced vibration | isolation | isolation | coupled oscillators | coupled oscillators | normal modes | normal modes | wave propagation | wave propagation | cartesian coordinates | cartesian coordinates | momentum | momentum | central force motion | central force motion

License

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12.800 Fluid Dynamics of the Atmosphere and Ocean (MIT)

Description

This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site.

Subjects

meteorology | climate | oceanography | Eulerian and Lagrangian kinematics | mass | momentum | energy | Vorticity | divergence Scaling | geostrophic approximation | Ekman layers | Vortex motion | fluid dynamics | atmospheric science | physical oceanography | ocean engineering | oceans | fluid flow | conservation equations | vortex flows | circulation | Earth | rotation | GFD kinematics | waves | Eulerian kinematics | Lagrangian kinematics

License

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2.76 Multi-Scale System Design (MIT) 2.76 Multi-Scale System Design (MIT)

Description

Multi-scale systems (MuSS) consist of components from two or more length scales (nano, micro, meso, or macro-scales). In MuSS, the engineering modeling, design principles, and fabrication processes of the components are fundamentally different. The challenge is to make these components so they are conceptually and model-wise compatible with other-scale components with which they interface. This course covers the fundamental properties of scales, design theories, modeling methods and manufacturing issues which must be addressed in these systems. Examples of MuSS include precision instruments, nanomanipulators, fiber optics, micro/nano-photonics, nanorobotics, MEMS (piezoelectric driven manipulators and optics), X-Ray telescopes and carbon nano-tube assemblies. Students master the materials Multi-scale systems (MuSS) consist of components from two or more length scales (nano, micro, meso, or macro-scales). In MuSS, the engineering modeling, design principles, and fabrication processes of the components are fundamentally different. The challenge is to make these components so they are conceptually and model-wise compatible with other-scale components with which they interface. This course covers the fundamental properties of scales, design theories, modeling methods and manufacturing issues which must be addressed in these systems. Examples of MuSS include precision instruments, nanomanipulators, fiber optics, micro/nano-photonics, nanorobotics, MEMS (piezoelectric driven manipulators and optics), X-Ray telescopes and carbon nano-tube assemblies. Students master the materials

Subjects

scale | scale | complexity | complexity | nano | micro | meso | or macro-scale | nano | micro | meso | or macro-scale | kinematics | kinematics | metrology | metrology | engineering modeling | motion | engineering modeling | motion | modeling | modeling | design | design | manufacture | manufacture | design principles | design principles | fabrication process | fabrication process | functional requirements | functional requirements | precision instruments | precision instruments | nanomanipulators | fiber optics | micro- photonics | nano-photonics | nanorobotics | MEMS | nanomanipulators | fiber optics | micro- photonics | nano-photonics | nanorobotics | MEMS | piezoelectric | transducer | actuator | sensor | piezoelectric | transducer | actuator | sensor | constraint | rigid constraint | flexible constraint | ride-flexible constraint | constraint | rigid constraint | flexible constraint | ride-flexible constraint | constaint-based design | constaint-based design | carbon nanotube | carbon nanotube | nanowire | nanowire | scanning tunneling microscope | scanning tunneling microscope | flexure | flexure | protein structure | protein structure | polymer structure | polymer structure | nanopelleting | nanopipette | nanowire | nanopelleting | nanopipette | nanowire | TMA pixel array | TMA pixel array | error modeling | error modeling | repeatability | repeatability

License

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12.800 Fluid Dynamics of the Atmosphere and Ocean (MIT) 12.800 Fluid Dynamics of the Atmosphere and Ocean (MIT)

Description

This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist. This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist.

Subjects

meteorology | meteorology | climate | climate | oceanography | oceanography | Eulerian and Lagrangian kinematics | Eulerian and Lagrangian kinematics | mass | mass | momentum | momentum | energy | energy | Vorticity | Vorticity | divergence Scaling | divergence Scaling | geostrophic approximation | geostrophic approximation | Ekman layers | Ekman layers | Vortex motion | Vortex motion

License

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2.007 Design and Manufacturing I (MIT) 2.007 Design and Manufacturing I (MIT)

Description

Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering.  See this MIT News story for more background, a photo gallery, and videos about this course. Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering.  See this MIT News story for more background, a photo gallery, and videos about this course.

Subjects

engineering design | engineering design | synthesis | synthesis | analysis | analysis | robustness | robustness | manufacturability | manufacturability | active learning | active learning | idea generation | idea generation | estimation | estimation | materials selection | materials selection | visual thinking | visual thinking | kinematics | kinematics | machine elements | machine elements | robotics | robotics | mechanical engineering | mechanical engineering | student work | student work | contest | contest

License

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12.802 Wave Motions in the Ocean and Atmosphere (MIT) 12.802 Wave Motions in the Ocean and Atmosphere (MIT)

Description

This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Also addressed are subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability. This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Also addressed are subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability.

Subjects

geophysical wave motion | geophysical wave motion | rotating | stratified | and rotating-stratified fluids | rotating | stratified | and rotating-stratified fluids | general wave concepts | general wave concepts | phase | phase | group velocity | group velocity | dynamics and kinematics of gravity waves | dynamics and kinematics of gravity waves | dispersion | dispersion | energy flux | energy flux | initial value problems | initial value problems | internal and inertial waves | internal and inertial waves | Kelvin | Kelvin | Poincare | Poincare | and Rossby waves | and Rossby waves | homogeneous and stratified fluids | homogeneous and stratified fluids | Laplace tidal equations | Laplace tidal equations | equatorial waves | equatorial waves | resonant interactions | resonant interactions | potential vorticity | potential vorticity | wave-mean flow interactions | wave-mean flow interactions | instability | instability | 12. Kelvin | Poincare | and Rossby waves | 12. Kelvin | Poincare | and Rossby waves | Kelvin | Poincare | and Rossby waves | Kelvin | Poincare | and Rossby waves | internal gravity waves | internal gravity waves | surface gravity waves | surface gravity waves | rotation | rotation | large-scale hydrostatic motions | large-scale hydrostatic motions | vertical structure equation | vertical structure equation | equatorial ?-plane | equatorial ?-plane | Stratified Quasi-Geostrophic Motion | Stratified Quasi-Geostrophic Motion

License

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16.13 Aerodynamics of Viscous Fluids (MIT) 16.13 Aerodynamics of Viscous Fluids (MIT)

Description

The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included. The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.

Subjects

aerodynamics | aerodynamics | viscous fluids | viscous fluids | viscosity | viscosity | fundamental theorem of kinematics | fundamental theorem of kinematics | convection | convection | vorticity | vorticity | strain | strain | Eulerian description | Eulerian description | Lagrangian description | Lagrangian description | conservation of mass | conservation of mass | continuity | continuity | conservation of momentum | conservation of momentum | stress tensor | stress tensor | newtonian fluid | newtonian fluid | circulation | circulation | Navier-Stokes | Navier-Stokes | similarity | similarity | dimensional analysis | dimensional analysis | thin shear later approximation | thin shear later approximation | TSL coordinates | TSL coordinates | boundary conditions | boundary conditions | shear later categories | shear later categories | local scaling | local scaling | Falkner-Skan flows | Falkner-Skan flows | solution techniques | solution techniques | finite difference methods | finite difference methods | Newton-Raphson | Newton-Raphson | integral momentum equation | integral momentum equation | Thwaites method | Thwaites method | integral kinetic energy equation | integral kinetic energy equation | dissipation | dissipation | asymptotic perturbation | asymptotic perturbation | displacement body | displacement body | transpiration | transpiration | form drag | form drag | stall | stall | interacting boundary layer theory | interacting boundary layer theory | stability | stability | transition | transition | small-perturbation | small-perturbation | Orr-Somemerfeld | Orr-Somemerfeld | temporal amplification | temporal amplification | spatial amplification | spatial amplification | Reynolds | Reynolds | Prandtl | Prandtl | turbulent boundary layer | turbulent boundary layer | wake | wake | wall layers | wall layers | inner variables | inner variables | outer variables | outer variables | roughness | roughness | Clauser | Clauser | Dissipation formula | Dissipation formula | integral closer | integral closer | turbulence modeling | turbulence modeling | transport models | transport models | turbulent shear layers | turbulent shear layers | compressible then shear layers | compressible then shear layers | compressibility | compressibility | temperature profile | temperature profile | heat flux | heat flux | 3D boundary layers | 3D boundary layers | crossflow | crossflow | lateral dilation | lateral dilation | 3D separation | 3D separation | constant-crossflow | constant-crossflow | 3D transition | 3D transition | compressible thin shear layers | compressible thin shear layers

License

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8.01L Physics I: Classical Mechanics (MIT) 8.01L Physics I: Classical Mechanics (MIT)

Description

8.01L is an introductory mechanics course, which covers all the topics covered in 8.01T. The class meets throughout the fall, and continues throughout the Independent Activities Period (IAP). 8.01L is an introductory mechanics course, which covers all the topics covered in 8.01T. The class meets throughout the fall, and continues throughout the Independent Activities Period (IAP).

Subjects

Introductory classical mechanics | Introductory classical mechanics | space | space | time | time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | forces | forces | static equilibrium | static equilibrium | particle dynamics | particle dynamics | conservation of momentum | conservation of momentum | relative inertial frames | relative inertial frames | non-inertial force | non-inertial force | work | work | potential energy | potential energy | conservation of energy | conservation of energy | ideal gas | ideal gas | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics | vibrational motion | vibrational motion | conservation of angular momentum | conservation of angular momentum | central force motions | central force motions | fluid mechanics | fluid mechanics | Technology-Enabled Active Learning | Technology-Enabled Active Learning

License

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8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe. This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe.

Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | General Relativity | General Relativity

License

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2.007 Design and Manufacturing I (MIT) 2.007 Design and Manufacturing I (MIT)

Description

This course develops students' competence and self-confidence as design engineers. Emphasis is on the creative design process bolstered by application of physical laws, and learning to complete projects on schedule and within budget. Synthesis, analysis, design robustness and manufacturability are emphasized. The subject relies on active learning via a major design-and-build project. Lecture topics include idea generation, estimation, concept selection, visual thinking and communication, kinematics of mechanisms, machine elements, design for manufacturing, basic electronics, and professional responsibilities and ethics. A required on-line evaluation is given at the beginning and the end of the course so students can assess their design knowledge. This course develops students' competence and self-confidence as design engineers. Emphasis is on the creative design process bolstered by application of physical laws, and learning to complete projects on schedule and within budget. Synthesis, analysis, design robustness and manufacturability are emphasized. The subject relies on active learning via a major design-and-build project. Lecture topics include idea generation, estimation, concept selection, visual thinking and communication, kinematics of mechanisms, machine elements, design for manufacturing, basic electronics, and professional responsibilities and ethics. A required on-line evaluation is given at the beginning and the end of the course so students can assess their design knowledge.

Subjects

creative design process | creative design process | Synthesis | Synthesis | analysis | analysis | design robustness | design robustness | manufacturability | manufacturability | active learning | active learning | idea generation | idea generation | estimation | estimation | concept selection | concept selection | visual thinking | visual thinking | kinematics | kinematics | machine elements | machine elements

License

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8.01T Physics I (MIT) 8.01T Physics I (MIT)

Description

This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | forces and equilibrium | forces and equilibrium | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | inertial forces and non-inertial frames | inertial forces and non-inertial frames | central force motions | central force motions | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics

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8.01 Physics I (MIT) 8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | central force motions | central force motions | inertial forces and non-inertial frames | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics | forces and equilibrium | forces and equilibrium | space | space | time | time | space-time | space-time | planar motion | planar motion | forces | forces | equilibrium | equilibrium | Newton?s laws | Newton?s laws | collisions | collisions | conservation laws | conservation laws | work | work | potential energy | potential energy | inertial forces | inertial forces | non-inertial forces | non-inertial forces | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics

License

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8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay. Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.

Subjects

Einstein's postulates | Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects and paradoxes | relativistic effects and paradoxes | Minkowski diagrams | Minkowski diagrams | invariants and four-vectors | invariants and four-vectors | momentum | energy and mass | momentum | energy and mass | particle collisions | particle collisions | Relativity and electricity | Relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | General Relativity | General Relativity | principle of equivalence | principle of equivalence | the Schwarzchild metric | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | gravitational red shift | particle trajectories | particle trajectories | light trajectories | light trajectories | invariants | invariants | four-vectors | four-vectors | momentum | momentum | energy | energy | mass | mass | relativistic effects | relativistic effects | paradoxes | paradoxes | electricity | electricity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Schwarzchild metric | Schwarzchild metric | geodesics | geodesics | Shaprio delay | Shaprio delay | relativistic kinematics | relativistic kinematics | relativistic dynamics | relativistic dynamics | electromagnetism | electromagnetism | hubble expansion | hubble expansion | universe | universe | equivalence principle | equivalence principle | curved space time | curved space time | Ether Theory | Ether Theory | constants | constants | speed of light | speed of light | c | c | graph | graph | pythagorem theorem | pythagorem theorem | triangle | triangle | arrows | arrows

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2.12 Introduction to Robotics (MIT) 2.12 Introduction to Robotics (MIT)

Description

This course provides an overview of robot mechanisms, dynamics, and intelligent controls. Topics include planar and spatial kinematics, and motion planning; mechanism design for manipulators and mobile robots, multi-rigid-body dynamics, 3D graphic simulation; control design, actuators, and sensors; wireless networking, task modeling, human-machine interface, and embedded software. Weekly laboratories provide experience with servo drives, real-time control, and embedded software. Students will design and fabricate working robotic systems in a group-based term project.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site. This course provides an overview of robot mechanisms, dynamics, and intelligent controls. Topics include planar and spatial kinematics, and motion planning; mechanism design for manipulators and mobile robots, multi-rigid-body dynamics, 3D graphic simulation; control design, actuators, and sensors; wireless networking, task modeling, human-machine interface, and embedded software. Weekly laboratories provide experience with servo drives, real-time control, and embedded software. Students will design and fabricate working robotic systems in a group-based term project.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.

Subjects

robot | robot | robot design | robot design | dynamics | dynamics | statics | statics | intelligent control | intelligent control | planar and spatial kinematics | planar and spatial kinematics | motion planning | motion planning | manipulator | manipulator | mobile robots | mobile robots | multi-rigid-body dynamics | multi-rigid-body dynamics | 3D graphic simulation | 3D graphic simulation | control design | control design | actuator | actuator | sensor | sensor | task modeling | task modeling | human-machine interface | human-machine interface | embedded software | embedded software | servo | servo | servomechanism | servomechanism | real-time control | real-time control | computer vision | computer vision | navigation | navigation | tele-robotics | tele-robotics | virtual reality | virtual reality

License

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6.838 Algorithms for Computer Animation (MIT) 6.838 Algorithms for Computer Animation (MIT)

Description

Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robo Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robo

Subjects

algorithms | algorithms | computer animation | computer animation | keyframing | keyframing | inverse kinematics | inverse kinematics | physical simulation | physical simulation | optimization | optimization | optimal control | optimal control | motion capture | motion capture | data-driven methods | data-driven methods

License

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16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.

Subjects

Curvilinear motion | carteian coordinates | dynamics | equations of motion | intrinsic coordinates | coordinate systems | work | energy | conservative forces | potential energy | linear impulse | mommentum | angular impulse | relative motion | rotating axes | translating axes | Newton's second law | inertial forces | accelerometers | Newtonian relativity | gravitational attraction | 2D rigid body kinematics | conservation laws for systems of particles | 2D rigid body dynamics | pendulums | 3D rigid body kinematics | 3d rigid body dynamics | inertia tensor | gyroscopic motion | torque-free motion | spin stabilization | variable mass systems | rocket equation | central foce motion | Keppler's laws | orbits | orbit transfer | vibration | spring mass systems | forced vibration | isolation | coupled oscillators | normal modes | wave propagation | cartesian coordinates | momentum | central force motion

License

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10.52 Mechanics of Fluids (MIT) 10.52 Mechanics of Fluids (MIT)

Description

This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows. This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows.

Subjects

fluid mechanics | fluid mechanics | continuum mechanics | continuum mechanics | kinematics | kinematics | macroscopic balances for linear momentum | macroscopic balances for linear momentum | macroscopic balances for angular momentum | macroscopic balances for angular momentum | the stress tensor | the stress tensor | creeping flows | creeping flows | lubrication approximation | lubrication approximation | boundary layer approximation | boundary layer approximation | linear stability theory | linear stability theory | simple turbulent flows | simple turbulent flows

License

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2.003SC Engineering Dynamics (MIT) 2.003SC Engineering Dynamics (MIT)

Description

Includes audio/video content: AV lectures. This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems. Includes audio/video content: AV lectures. This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.

Subjects

dynamics and vibrations | dynamics and vibrations | lumped-parameter models | lumped-parameter models | kinematics | kinematics | momentum | momentum | systems of particles and rigid bodies | systems of particles and rigid bodies | work-energy concepts | work-energy concepts | virtual displacements and virtual work | virtual displacements and virtual work | Lagrange's equations | Lagrange's equations | equations of motion | equations of motion | linear stability analysis | linear stability analysis | free and forced vibration | free and forced vibration | linear multi-degree of freedom models | linear multi-degree of freedom models | matrix eigenvalue problems | matrix eigenvalue problems

License

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2.007 Design and Manufacturing I (MIT) 2.007 Design and Manufacturing I (MIT)

Description

Develops students' competence and self-confidence as design engineers. Emphasis on the creative design process bolstered by application of physical laws, and learning to complete projects on schedule and within budget. Synthesis, analysis, design 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 and communication, kinematics of mechanisms, machine elements, design for manufacturing, basic electronics, and professional responsibilities and ethics. A required on-line evaluation is given at the beginning and the end of the course so students can assess their design knowledge. Develops students' competence and self-confidence as design engineers. Emphasis on the creative design process bolstered by application of physical laws, and learning to complete projects on schedule and within budget. Synthesis, analysis, design 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 and communication, kinematics of mechanisms, machine elements, design for manufacturing, basic electronics, and professional responsibilities and ethics. A required on-line evaluation is given at the beginning and the end of the course so students can assess their design knowledge.

Subjects

creative design process | creative design process | Synthesis | Synthesis | analysis | analysis | design robustness | design robustness | manufacturability | manufacturability | active learning | active learning | idea generation | idea generation | estimation | estimation | concept selection | concept selection | visual thinking | visual thinking | kinematics | kinematics | machine elements | machine elements

License

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12.802 Wave Motion in the Ocean and the Atmosphere (MIT) 12.802 Wave Motion in the Ocean and the Atmosphere (MIT)

Description

This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc.

Subjects

ocean | ocean | atmosphere | atmosphere | wave motion | wave motion | wave kinematics | wave kinematics | gravity waves | gravity waves | Kelvin waves | Kelvin waves | Rossby waves | Rossby waves | wave equation | wave equation | Laplace?s tidal equations | Laplace?s tidal equations | wave-mean flow interactions | wave-mean flow interactions

License

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6.838 Algorithms for Computer Animation (MIT) 6.838 Algorithms for Computer Animation (MIT)

Description

Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robo Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robo

Subjects

algorithms | algorithms | computer animation | computer animation | keyframing | keyframing | inverse kinematics | inverse kinematics | physical simulation | physical simulation | optimization | optimization | optimal control | optimal control | motion capture | motion capture | data-driven methods | data-driven methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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2.12 Introduction to Robotics (MIT) 2.12 Introduction to Robotics (MIT)

Description

This course provides an overview of robot mechanisms, dynamics, and intelligent controls. Topics include planar and spatial kinematics, and motion planning; mechanism design for manipulators and mobile robots, multi-rigid-body dynamics, 3D graphic simulation; control design, actuators, and sensors; wireless networking, task modeling, human-machine interface, and embedded software. Weekly laboratories provide experience with servo drives, real-time control, and embedded software. Students will design and fabricate working robotic systems in a group-based term project. This course provides an overview of robot mechanisms, dynamics, and intelligent controls. Topics include planar and spatial kinematics, and motion planning; mechanism design for manipulators and mobile robots, multi-rigid-body dynamics, 3D graphic simulation; control design, actuators, and sensors; wireless networking, task modeling, human-machine interface, and embedded software. Weekly laboratories provide experience with servo drives, real-time control, and embedded software. Students will design and fabricate working robotic systems in a group-based term project.

Subjects

robot | robot | robot design | robot design | rescue | rescue | recovery | recovery | automation | automation | dynamics | dynamics | statics | statics | intelligent control | intelligent control | planar and spatial kinematics | planar and spatial kinematics | motion planning | motion planning | manipulator | manipulator | mobile robots | mobile robots | multi-rigid-body dynamics | multi-rigid-body dynamics | 3D graphic simulation | 3D graphic simulation | control design | control design | actuator | actuator | sensor | sensor | task modeling | task modeling | human-machine interface | human-machine interface | embedded software | embedded software | servo | servo | servomechanism | servomechanism | real-time control | real-time control | computer vision | computer vision | navigation | navigation | tele-robotics | tele-robotics | virtual reality | virtual reality

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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13.013J Dynamics and Vibration (MIT) 13.013J Dynamics and Vibration (MIT)

Description

Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.

Subjects

umped-parameter models | umped-parameter models | lumped-parameter models | lumped-parameter models | mechanical systems | mechanical systems | Three-dimensional particle kinematics | Three-dimensional particle kinematics | Force-momentum formulation | Force-momentum formulation | Newton-Euler equations | Newton-Euler equations | Work-enery (variational) formulation | Work-enery (variational) formulation | systems particles | systems particles | rigid bodies (indirect method) | rigid bodies (indirect method) | Virtual displacements | Virtual displacements | Lagrange's equations | Lagrange's equations | Linear stability analysis | Linear stability analysis | 1.053J | 1.053J | 13.013 | 13.013 | 1.053 | 1.053

License

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8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity. Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity.

Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | ime dilation | ime dilation | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | General Relativity | General Relativity

License

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