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Toroidal Helical Orbits

  1. Nov 23, 2007 #1
    Does anyone know the equation for the helical path length around a torus?
    I need an analytical expression, not an approximation.

  2. jcsd
  3. Nov 23, 2007 #2

    Chris Hillman

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    Science Advisor

    Hint: write a parameterization of your surface (torus of cross-section radius r centered on a circle with radius R > r). Find the tangent vectors to this surface by differentiating wrt the two parameters of your parameterization. Consider a linear combination with undetermined coefficients to obtain a vector field lying in the torus. (Did you have a particular "pitch" in mind?) Find the integral curves.
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