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Classical Mechanics: A Computational Approach

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; ...

Start Date: Sep 01, 2008
Cost: Free

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Overview

Description

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.

Details

  • Dates: 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

Provider Overview

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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