"Classical Mechanics: A Computational Approach, Fall 2008"
- Author:
- Sussman, Gerald, Wisdom, Jack
- Subject:
- Science and Technology
- Institution Name:
- M.I.T.
- Collection:
- MIT OpenCourseWare
- Grade Level:
- Post-secondary
- Abstract:
" We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: 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; properties of chaotic motion. Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis."
- Languages:
- English
- Material Type:
- Full Course, Training Materials
- Media Format:
- Text/HTML, Downloadable docs
- Conditions of Use:
-
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Creative Commons Attribution-NonCommercial-ShareAlike 3.0
Comments