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Homework Help: Unit normal vector

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img171.imageshack.us/img171/5997/76283103.png [Broken]

    3. The attempt at a solution

    I think a good place to start is with the definition of regular.
    My definition is: σ is regular if ∂σ/∂s and ∂σ/∂v are linearly independent.

    Want to confirm I'm on the right track before going further!
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 9, 2009 #2
    help anyone!?
  4. Sep 9, 2009 #3


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    Gold Member

    regularity means that:
    [tex]d\sigma =/=0[/tex] for any s and v which is the same as what you wrote, i.e equivalent statements.
    And you know how to find the normal to sigma, just multiply by scalar product N with the tangent of sigma, which is the derivative, and then divide by its norm.
  5. Sep 9, 2009 #4
    ok, so after showing that sigma is regular, I want to find the unit vector normal (as you said above).

    Found my equation in the text, just wondering if the notation is correct
    http://img3.imageshack.us/img3/8527/11604435.png [Broken]
    Last edited by a moderator: May 4, 2017
  6. Sep 11, 2009 #5
    to the top again
  7. Sep 12, 2009 #6
    Well, I'm assuming the definition posted 2 posts above is correct, so then I proceed to evaluate ∂σ/∂s and ∂σ/∂v..

    ∂σ/∂s = ∂γ/∂s + r[(dn/ds)(cos v) + (db/ds)(sinv)]


    ∂σ/∂v = r[-n(s)sin v + b(s)cosv]

    But now I'm wondering, how do I cross product these two if they are not vectors!!
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