主题目录

  • 课程介绍( Course Introduction)

    • University: Massachusetts Institute of Technology
      Instructors:
      Prof. Gerald Sussman
      Prof. Jack Wisdom
      Course Number:12.620J / 6.946J / 8.351J
      Level: Graduate
      Course 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 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.

  • 教学大纲(Syllabus)

    Grades

    The grades for this subject will be determined by a combination of classroom participation, homework, and laboratory work. There are no examinations in this subject.

    Collaborative Work

    Many people learn more effectively when they study in small groups and cooperate in various other ways on homework. We are very much in favor of this kind of cooperation so long as all participants actively involve themselves in all aspects of the work. When you hand in a paper with your name on it we assume that you are certifying it as your work and that you were involved in all aspects of it. Even if you work with others you should do the writeup yourself, and you should indicate the names of any collaborators for each part of the assignment.