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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

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12.620J Classical Mechanics: A Computational Approach (MIT) 12.620J Classical Mechanics: A Computational Approach (MIT)

Description

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov 12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov

Subjects

classical mechanics | classical mechanics | phase space | phase space | computation | computation | Lagrangian formulation | Lagrangian formulation | action | action | variational principles | variational principles | equations of motion | equations of motion | Hamilton's principle | Hamilton's principle | conserved quantities | conserved quantities | rigid bodies and tops | rigid bodies and tops | Hamiltonian formulation | Hamiltonian formulation | canonical equations | canonical equations | surfaces of section | surfaces of section | chaos | chaos | canonical transformations | canonical transformations | generating functions | generating functions | Liouville's theorem | Liouville's theorem | Poincar? integral invariants | Poincar? integral invariants | Poincar?-Birkhoff | Poincar?-Birkhoff | KAM theorem | KAM theorem | invariant curves | invariant curves | cantori | cantori | nonlinear resonances | nonlinear resonances | resonance overlap | resonance overlap | transition to chaos | transition to chaos | chaotic motion | chaotic motion | 12.620 | 12.620 | 6.946 | 6.946 | 8.351 | 8.351

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8.09 Classical Mechanics II (MIT) 8.09 Classical Mechanics II (MIT)

Description

This course provides a formal introduction to classical mechanics. Topics include Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also provides an extension to continuous and relativistic systems and classical electrodynamics.AcknowledgementsProfessor Wyslouch acknowledges the contributions of MIT Professor Christoph Paus to the development of the 8.09 materials. This course provides a formal introduction to classical mechanics. Topics include Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also provides an extension to continuous and relativistic systems and classical electrodynamics.AcknowledgementsProfessor Wyslouch acknowledges the contributions of MIT Professor Christoph Paus to the development of the 8.09 materials.

Subjects

classical mechanics | classical mechanics | Euler-Lagrange equations | Euler-Lagrange equations | Hamilton's equations of motion | Hamilton's equations of motion | perturbation theory | perturbation theory | Noether's theorem | Noether's theorem | continuous and relativistic systems | continuous and relativistic systems | classical electrodynamics | classical electrodynamics

License

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6.641 Electromagnetic Fields, Forces, and Motion (MIT) 6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc. 6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc.

Subjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomena

License

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13.49 Maneuvering and Control of Surface and Underwater Vehicles (MIT) 13.49 Maneuvering and Control of Surface and Underwater Vehicles (MIT)

Description

This course is about maneuvering motions of surface and underwater vehicles. Topics covered include: 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. The course also deals with stability of motion, principles of multivariable automatic control, optimal control, Kalman filtering, and loop transfer recovery. We will also explore applications chosen from autopilots for surface vehicles; towing in open seas; and remotely operated vehicles. This course is about maneuvering motions of surface and underwater vehicles. Topics covered include: 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. The course also deals with stability of motion, principles of multivariable automatic control, optimal control, Kalman filtering, and loop transfer recovery. We will also explore applications chosen from autopilots for surface vehicles; towing in open seas; and remotely operated vehicles.

Subjects

Maneuvering | Maneuvering | motion | motion | surface and underwater vehicles | surface and underwater vehicles | Derivation of equations of motion | Derivation of equations of motion | hydrodynamic coefficients | hydrodynamic coefficients | Memory effects | Memory effects | Linear and nonlinear forms | Linear and nonlinear forms | Control surfaces | Control surfaces | modeling and design | modeling and design | Engine | Engine | propulsor | propulsor | transmission systems modeling | transmission systems modeling | simulation | simulation | Stability of motion | Stability of motion | multivariable automatic control | multivariable automatic control | Optimal control | Optimal control | Kalman filtering | Kalman filtering | loop transfer recovery | loop transfer recovery | autopilots for surface vehicles | autopilots for surface vehicles | towing in open seas | towing in open seas | remotely operated vehicles | remotely operated vehicles | 2.154 | 2.154

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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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6.641 Electromagnetic Fields, Forces, and Motion (MIT) 6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

Includes audio/video content: AV faculty introductions. This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and Includes audio/video content: AV faculty introductions. This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and

Subjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomena

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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2.003J Dynamics and Control I (MIT) 2.003J Dynamics and Control I (MIT)

Description

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. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems. 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. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

Subjects

dynamics and vibrations of lumped-parameter models | dynamics and vibrations of lumped-parameter models | mechanical systems | mechanical systems | Kinematics | Kinematics | Force-momentum formulation | Force-momentum formulation | systems of particles | systems of particles | rigid bodies in planar motion | rigid bodies in planar motion | Work-energy concepts | Work-energy concepts | Virtual displacements | Virtual displacements | virtual work | virtual work | Lagrange's equations | Lagrange's equations | Linearization of equations of motion | Linearization of equations of motion | Linear stability analysis | Linear stability analysis | Free vibration | Free vibration | forced vibration | forced vibration | linear multi-degree of freedom models | linear multi-degree of freedom models | matrix eigenvalue problems | matrix eigenvalue problems | numerical methods | numerical methods | MATLAB | MATLAB

License

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2.154 Maneuvering and Control of Surface and Underwater Vehicles (13.49) (MIT) 2.154 Maneuvering and Control of Surface and Underwater Vehicles (13.49) (MIT)

Description

This course is about maneuvering motions of surface and underwater vehicles. Topics covered include: 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. The course also deals with stability of motion, principles of multivariable automatic control, optimal control, Kalman filtering, and loop transfer recovery. We will also explore applications chosen from autopilots for surface vehicles; towing in open seas; and remotely operated vehicles. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.49. In 2005, ocean engineering subjects became part of Co This course is about maneuvering motions of surface and underwater vehicles. Topics covered include: 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. The course also deals with stability of motion, principles of multivariable automatic control, optimal control, Kalman filtering, and loop transfer recovery. We will also explore applications chosen from autopilots for surface vehicles; towing in open seas; and remotely operated vehicles. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.49. In 2005, ocean engineering subjects became part of Co

Subjects

Maneuvering | Maneuvering | motion | motion | surface and underwater vehicles | surface and underwater vehicles | Derivation of equations of motion | Derivation of equations of motion | hydrodynamic coefficients | hydrodynamic coefficients | Memory effects | Memory effects | Linear and nonlinear forms | Linear and nonlinear forms | Control surfaces | Control surfaces | modeling and design | modeling and design | Engine | Engine | propulsor | propulsor | transmission systems modeling | transmission systems modeling | simulation | simulation | Stability of motion | Stability of motion | multivariable automatic control | multivariable automatic control | Optimal control | Optimal control | Kalman filtering | Kalman filtering | loop transfer recovery | loop transfer recovery | autopilots for surface vehicles | autopilots for surface vehicles | towing in open seas | towing in open seas | remotely operated vehicles | remotely operated vehicles

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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6.641 Electromagnetic Fields, Forces, and Motion (MIT) 6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams. 6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.

Subjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomena

License

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8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

License

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8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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18.354J Nonlinear Dynamics II: Continuum Systems (MIT) 18.354J Nonlinear Dynamics II: Continuum Systems (MIT)

Description

This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling. This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling.

Subjects

continuum systems | continuum systems | mathematical modeling | mathematical modeling | diffusion equation | diffusion equation | equations of motion | equations of motion | nonlinear partial differential equations | nonlinear partial differential equations | calculus of variations | calculus of variations | Brachistochrone curve | Brachistochrone curve | soap films | soap films | hydrodynamics | hydrodynamics | Navier-Stokes | Navier-Stokes | solitons | solitons | surface tension | surface tension | waves | waves | conformal maps | conformal maps | airfoils | airfoils

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8.09 Classical Mechanics (MIT) 8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics. This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | classical mechanics | Euler-Lagrange equations | Euler-Lagrange equations | Hamilton's equations of motion | Hamilton's equations of motion | perturbation theory | perturbation theory | Noether's theorem | Noether's theorem | continuous and relativistic systems | continuous and relativistic systems | classical electrodynamics | classical electrodynamics

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20.430J Fields, Forces, and Flows in Biological Systems (MIT) 20.430J Fields, Forces, and Flows in Biological Systems (MIT)

Description

This course covers the fundamental driving forces for transport—chemical gradients, electrical interactions, and fluid flow—as applied to the biology and biophysics of molecules, cells, and tissues. This course covers the fundamental driving forces for transport—chemical gradients, electrical interactions, and fluid flow—as applied to the biology and biophysics of molecules, cells, and tissues.

Subjects

diffusion | diffusion | molecular diffusion | molecular diffusion | diffusion-reaction | diffusion-reaction | conduction | conduction | convection | convection | biological systems | biological systems | fields | fields | electrical double layers | electrical double layers | Maxwell stress tensor | Maxwell stress tensor | physiological systems | physiological systems | fluid | fluid | solid | solid | equations of motion | equations of motion | case study | case study | electrode interfaces | electrode interfaces | transduction | transduction | random walk | random walk | Stokes-Einstein | Stokes-Einstein | Fick's laws | Fick's laws | reaction | reaction | Damköhler number | Damköhler number

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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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

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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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

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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6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.

Subjects

electromagnetic | electromagnetic field | forces | motion | electric | magnetic | quasistatic | Maxwell's equations | dielectric | conduction | magnetization | boundary value problems | force densities | stress tensors | polarization | thermodynamics | equations of motion | energy conservation | synchronous | induction | commutator machines | sensors | transducers | microelectromechanical systems | electromechanical waves | charge transport phenomena

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 https://ocw.mit.edu/terms/index.htm

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8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

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 https://ocw.mit.edu/terms/index.htm

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8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

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 https://ocw.mit.edu/terms/index.htm

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Core Physics PBL – White Knuckle Ride.

Description

You will have four laboratory sessions to perform the experiments, as well as two workshops with facilitators. For each of the workshops you should prepare answers to set question, which will be marked at the workshops. These workshop questions are designed to support the practical work by providing ideas and relevant theory.

Subjects

sfsoer | ukoer | friction | equations of motion | kinetic energy | potential energy | Physical sciences | F000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

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 https://ocw.mit.edu/terms/index.htm

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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

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 https://ocw.mit.edu/terms/index.htm

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12.620J Classical Mechanics: A Computational Approach (MIT)

Description

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov

Subjects

classical mechanics | phase space | computation | Lagrangian formulation | action | variational principles | equations of motion | Hamilton's principle | conserved quantities | rigid bodies and tops | Hamiltonian formulation | canonical equations | surfaces of section | chaos | canonical transformations | generating functions | Liouville's theorem | Poincar? integral invariants | Poincar?-Birkhoff | KAM theorem | invariant curves | cantori | nonlinear resonances | resonance overlap | transition to chaos | chaotic motion | 12.620 | 6.946 | 8.351

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 https://ocw.mit.edu/terms/index.htm

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8.09 Classical Mechanics II (MIT)

Description

This course provides a formal introduction to classical mechanics. Topics include Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also provides an extension to continuous and relativistic systems and classical electrodynamics.AcknowledgementsProfessor Wyslouch acknowledges the contributions of MIT Professor Christoph Paus to the development of the 8.09 materials.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

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 https://ocw.mit.edu/terms/index.htm

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