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The shortest distance along cone

  1. May 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Obtain an integral formula for the length of a curve p(theta) along a right cone. use spherical coordinates p and theta.
    Answer: L = integral from -pi/2 to pi/2 of sqrt(p'^2 + p^2/R^2)d(theta)

    2. Relevant equations
    p is distance from origin
    altitude a, radius 1, cone's point is at origin, R=sqrt(a^2+1)

    3. The attempt at a solution
    I know ds^2 = dp^2 +sin^2p d(theta)^2 on spherical coordinates, but don't know how to begin translating that into the answer above
    Last edited: May 19, 2009
  2. jcsd
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