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Homework Help: L = r X p - in Sphereical Coordinates

  1. Feb 18, 2010 #1
    L = r X p --- in Sphereical Coordinates

    1. The problem statement, all variables and given/known data
    Express in vector form angular momentum in spherical coordinates.

    [tex]\rho[/tex] is the distance from the origin to the point
    [tex]\phi[/tex] is the angle made in the Cesarean x-y plane counter-clockwise from the positive x-axis
    [tex]\theta[/tex] is the angle downward from the z-axis


    2. Relevant equations



    3. The attempt at a solution
    Is it as simple as

    r = [tex]\rho[/tex][tex]\hat{\rho}[/tex] + [tex]\phi[/tex][tex]\hat{\phi}[/tex] + [tex]\theta[/tex][tex]\hat{\theta}[/tex]
    and
    v = [tex]\dot{\rho}[/tex][tex]\hat{\rho}[/tex] + [tex]\rho[/tex]sin([tex]\theta[/tex])[tex]\dot{\phi}[/tex][tex]\hat{\phi}[/tex] + [tex]\rho[/tex][tex]\dot{\theta}[/tex][tex]\hat{\theta}[/tex]
    ?
     
  2. jcsd
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