Classical Mechanics: A Computational Approach's Full Profile
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 Poincar integral invariants; Poincar-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.
Sep 01, 2008
to Dec 20, 2008
Days of the Week:
Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
- Level of Difficulty: Beginner
- Size: Massive Open Online Course
- Instructors: Prof. Jack Wisdom, Prof. Gerald Sussman
- Cost: Free
- Institution: MIT OCW
About MIT OCW:
MIT OpenCourseWare (OCW) is a web-based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.
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MIT OpenCourseWare (MIT OCW) is an initiative of the Massachusetts Institute of Technology (MIT) to put all of the educational materials from its undergraduate- and graduate-level courses online, partly free and openly available to anyone, anywhere.