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Hamilton-Jacobi homework problem

  1. Nov 26, 2009 #1
    1. The problem statement, all variables and given/known data

    It is well known that for a conservative motion there is a potential.
    This potential is a function of coordinates only.

    Prove this.

    2. Relevant equations



    3. The attempt at a solution

    I think you have to take a definition of conservative motion then for example prove that for such a motion, the rotational forces equals to 0 and they don't depend on time, then it will mean that there is a potential field.


    What is the equation for conservative motion?
     
  2. jcsd
  3. Nov 26, 2009 #2
    Re: Hamilton-Jacobi

    I guess we suppose that the general form of the force field is F=F(q,p,t)
     
  4. Nov 27, 2009 #3
    Re: Hamilton-Jacobi

    In general, a force is conservative iff the path integral of F around some closed path is equal to 0. This is equivalent to stating that the curl of F = 0.
     
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