12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002
Classical mechanics in a computational framework. Lagrangian formulation. Action, variational principles. Hamilton's principle. Conserved quantities. Hamiltonian formulation. Surfaces of section. Chaos. Liouville's theorem and Poincar, integral invariants. Poincar,-Birkhoff and KAM theorem...
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| Format: | Learning Object |
| Language: | en-US |
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2002
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| Online Access: | http://hdl.handle.net/1721.1/52321 |
| _version_ | 1826212200925102080 |
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| author | Sussman, Gerald Jay Wisdom, Jack |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Sussman, Gerald Jay Wisdom, Jack |
| author_sort | Sussman, Gerald Jay |
| collection | MIT |
| description | Classical mechanics in a computational framework. Lagrangian formulation. Action, variational principles. Hamilton's principle. Conserved quantities. Hamiltonian formulation. Surfaces of section. Chaos. Liouville's theorem and Poincar, integral invariants. Poincar,-Birkhoff and KAM theorems. Invariant curves. Cantori. Nonlinear resonances. Resonance overlap and transition to chaos. Properties of chaotic motion. Transport, diffusion, mixing. Symplectic integration. Adiabatic invariants. Many-dimensional systems, Arnold diffusion. Extensive use of computation to capture methods, for simulation, and for symbolic analysis. From the course home page: Course 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 overlap and transition to chaos, and properties of chaotic motion. Ideas are illustrated and supported with physical examples. There is extensive use of computing to capture methods, for simulation, and for symbolic analysis. |
| first_indexed | 2024-09-23T15:17:57Z |
| format | Learning Object |
| id | mit-1721.1/52321 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2025-03-10T13:01:12Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | mit-1721.1/523212025-02-26T17:35:10Z 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 Classical Mechanics: A Computational Approach Sussman, Gerald Jay Wisdom, Jack Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Physics 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 Poincaré integral invariants Poincaré-Birkhoff KAM theorem invariant curves cantori nonlinear resonances resonance overlap transition to chaos chaotic motion 12.620J 6.946J 8.351J 12.620 6.946 8.351 Mechanics Classical mechanics in a computational framework. Lagrangian formulation. Action, variational principles. Hamilton's principle. Conserved quantities. Hamiltonian formulation. Surfaces of section. Chaos. Liouville's theorem and Poincar, integral invariants. Poincar,-Birkhoff and KAM theorems. Invariant curves. Cantori. Nonlinear resonances. Resonance overlap and transition to chaos. Properties of chaotic motion. Transport, diffusion, mixing. Symplectic integration. Adiabatic invariants. Many-dimensional systems, Arnold diffusion. Extensive use of computation to capture methods, for simulation, and for symbolic analysis. From the course home page: Course 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 overlap and transition to chaos, and properties of chaotic motion. Ideas are illustrated and supported with physical examples. There is extensive use of computing to capture methods, for simulation, and for symbolic analysis. 2002-12 Learning Object 12.620J-Fall2002 local: 12.620J local: 6.946J local: 8.351J local: IMSCP-MD5-30d9902167a02eb51d494aa347d1a729 http://hdl.handle.net/1721.1/52321 en-US Usage Restrictions: This site (c) Massachusetts Institute of Technology 2003. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license"). The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. text/html Fall 2002 |
| spellingShingle | 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 Poincaré integral invariants Poincaré-Birkhoff KAM theorem invariant curves cantori nonlinear resonances resonance overlap transition to chaos chaotic motion 12.620J 6.946J 8.351J 12.620 6.946 8.351 Mechanics Sussman, Gerald Jay Wisdom, Jack 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title_full | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title_fullStr | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title_full_unstemmed | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title_short | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 |
| title_sort | 12 620j 6 946j 8 351j classical mechanics a computational approach fall 2002 |
| topic | 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 Poincaré integral invariants Poincaré-Birkhoff KAM theorem invariant curves cantori nonlinear resonances resonance overlap transition to chaos chaotic motion 12.620J 6.946J 8.351J 12.620 6.946 8.351 Mechanics |
| url | http://hdl.handle.net/1721.1/52321 |
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