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Hamilton-Jacobi Equation

  1. May 30, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m moves in the forcefield whose potential in spherical coordinates is V= - (K cos θ)/r2
    Whrite the Hamilton-Jacobi equation describing its motion.

    2. Relevant equations
    H=(pr2 / 2m)+ (pθ2 / 2mr2)+(pφ2 / 2mr2sin 2θ) + V

    3. The attempt at a solution
    I don't know how to do it because it's the first exercise of its kind to I have to solve
     
  2. jcsd
  3. May 30, 2015 #2
    If kinetic energy is ##T(\dot{x}_i)## only and potential energy is ##V(x_i)## only, then:
    $$ \frac{d\mathbf{p}_i}{dt} = -\frac{\partial{U}}{\partial{x}_i} $$
    and think about what is the partial derivation on some direction. U is the potential energy.
     
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