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12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002

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Show simple item record Sussman, Gerald Jay en_US Wisdom, Jack en_US
dc.coverage.temporal Fall 2002 en_US 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.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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