12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002
dc.contributor.author | Sussman, Gerald Jay | en_US |
dc.contributor.author | Wisdom, Jack | en_US |
dc.coverage.temporal | Fall 2002 | en_US |
dc.date.issued | 2002-12 | |
dc.identifier | 12.620J-Fall2002 | |
dc.identifier | local: 12.620J | |
dc.identifier | local: 6.946J | |
dc.identifier | local: 8.351J | |
dc.identifier | local: IMSCP-MD5-30d9902167a02eb51d494aa347d1a729 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/52321 | |
dc.description.abstract | 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. | en_US |
dc.language | en-US | en_US |
dc.rights.uri | 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. | en_US |
dc.subject | classical mechanics | en_US |
dc.subject | phase space | en_US |
dc.subject | computation | en_US |
dc.subject | Lagrangian formulation | en_US |
dc.subject | action | en_US |
dc.subject | variational principles | en_US |
dc.subject | equations of motion | en_US |
dc.subject | Hamilton's principle | en_US |
dc.subject | conserved quantities | en_US |
dc.subject | rigid bodies and tops | en_US |
dc.subject | Hamiltonian formulation | en_US |
dc.subject | canonical equations | en_US |
dc.subject | surfaces of section | en_US |
dc.subject | chaos | en_US |
dc.subject | canonical transformations | en_US |
dc.subject | generating functions | en_US |
dc.subject | Liouville's theorem | en_US |
dc.subject | Poincaré integral invariants | en_US |
dc.subject | Poincaré-Birkhoff | en_US |
dc.subject | KAM theorem | en_US |
dc.subject | invariant curves | en_US |
dc.subject | cantori | en_US |
dc.subject | nonlinear resonances | en_US |
dc.subject | resonance overlap | en_US |
dc.subject | transition to chaos | en_US |
dc.subject | chaotic motion | en_US |
dc.subject | 12.620J | en_US |
dc.subject | 6.946J | en_US |
dc.subject | 8.351J | en_US |
dc.subject | 12.620 | en_US |
dc.subject | 6.946 | en_US |
dc.subject | 8.351 | en_US |
dc.subject | Mechanics | en_US |
dc.title | 12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002 | en_US |
dc.title.alternative | Classical Mechanics: A Computational Approach | en_US |
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