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A How do you find S?

  1. Nov 30, 2016 #1
    How do you find the Hamilton principal function, S? From the Hamilton Jacobi equation if it is not given.
     
  2. jcsd
  3. Nov 30, 2016 #2

    jedishrfu

    Staff: Mentor

    Here's a discussion of the HJE where it mentions using separation of variables to find the principal function S. It further says the S in this case is considered the most useful solution.

    https://en.wikipedia.org/wiki/Hamilton–Jacobi_equation

    and here's an example of where the technique was used:

    http://www.physics.usu.edu/Wheeler/ClassicalMechanics/CMHamiltonJacobi.pdf

    and some more detailed treatments:

    http://www.physics.rutgers.edu/~shapiro/507/book7_2.pdf

    and

    https://www.pdx.edu/nanogroup/sites/www.pdx.edu.nanogroup/files/Chapter_4__Hamilton_Variational_principle__Hamilton Jacobi_Eq_Classical_Mechanics_1.pdf

    Hopefully someone will provide a more direct answer than this.
     
  4. Nov 30, 2016 #3
    I like the fact that they use for the time independent treatment for S. Is there one for the time dependent one?
     
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