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Action-angle Coordinates

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Avatar for Adrian Price-Whelan Adrian Price-Whelan
October 09, 2014
Science
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180

Action-angle Coordinates

A semi-casual introduction to Action-angle coordinates in Hamiltonian dynamics.

Avatar for Adrian Price-Whelan

Adrian Price-Whelan

October 09, 2014
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Transcript

  1. ACTION-ANGLE COORDINATES Adrian Price-Whelan

  2. None
  3. None

  4. n second order 2n first order

  5. n=3, 6D phase-space

  6. Integrable systems There exist n independent integrals of motion In

    2n-dimensional phase-space:

  7. Integrable systems There exist n independent integrals of motion Motion

    is confined to an n-dimensional manifold In 2n-dimensional phase-space:

  8. Integrable systems Bounded motion periodicity

  9. Integrable systems What if…

  10. Integrable systems

  11. Action-angle coords.

  12. Action-angle coords.

  13. Action-angle coords.

  14. None
  15. None
  16. None
  17. None
  18. None
  19. None

  20. cool. SO WHAT?

  21. Tidal stream formation Hessian

  22. Tidal stream formation

  23. Position Velocity

  24. Angles Actions

  25. so how do we find actions?

  26. This is not a solved problem!

  27. Kaasalainen & Binney McGill & Binney Sanders & Binney Bovy