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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Finish reading Chapter 6 Canonical transformations Hamilton-Jacobi formalism. Review: Liouville’s theorem:

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. PHY 711 Classical Mechanics and Mathematical Methods • 10-10:50 AM MWF Olin 103 • Plan for Lecture 13: • Finish reading Chapter 6 • Canonical transformations • Hamilton-Jacobi formalism PHY 711 Fall 2013 -- Lecture 13

  2. PHY 711 Fall 2013 -- Lecture 13

  3. PHY 711 Fall 2013 -- Lecture 13

  4. PHY 711 Fall 2013 -- Lecture 13

  5. Review: Liouville’stheorem: Imagine a collection of particles obeying the Canonical equations of motion in phase space. PHY 711 Fall 2013 -- Lecture 13

  6. Proof of Liouville’e theorem: PHY 711 Fall 2013 -- Lecture 13

  7. PHY 711 Fall 2013 -- Lecture 13

  8. 0 PHY 711 Fall 2013 -- Lecture 13

  9. Notion of “Canonical” distributions PHY 711 Fall 2013 -- Lecture 13

  10. Note that it is conceivable that if we were extraordinarily clever, we could find all of the constants of the motion! PHY 711 Fall 2013 -- Lecture 13

  11. PHY 711 Fall 2013 -- Lecture 13

  12. Note that it is conceivable that if we were extraordinarily clever, we could find all of the constants of the motion! Possible solution – Hamilton-Jacobi theory: PHY 711 Fall 2013 -- Lecture 13

  13. PHY 711 Fall 2013 -- Lecture 13

  14. 0 0 0 PHY 711 Fall 2013 -- Lecture 13

  15. 0 0 0 PHY 711 Fall 2013 -- Lecture 13

  16. Differential equation for S: PHY 711 Fall 2013 -- Lecture 13

  17. Continued: PHY 711 Fall 2013 -- Lecture 13

  18. Continued: PHY 711 Fall 2013 -- Lecture 13

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