12.620J / 6.946J / 8.351J Classical Mechanics: A Computational Approach, Fall 2002
Name
12-620JFall-2002/OcwWeb/Earth--Atmospheric--and-Planetary-Sciences/12-620JClassical-Mechanics--A-Computational-ApproachFall2002/CourseHome/index.htm
Size
15.22 KB
Format
HTML
Checksum (MD5)
97bb9fcad4f18b43061879896fd2b80a
Author(s)
Sussman, Gerald Jay
Wisdom, Jack
Alternative Title
Classical Mechanics: A Computational Approach
Date Issued
December 2002
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.
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
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
MIT Department
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
Terms of Use
Persistent DSpace Link
