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Proving dN/ds=−κT+τB

  1. Jul 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Currently revising for a differential geometry exam. The question I am working on is one of those types where the next part of the question follows from the last. I've gotten to the point where I have proven T⋅dNds=−κ,

    2. Relevant equations

    The next part is where I got stuck, which is to prove dN/ds=−κT+τB. I looked at the mark scheme

    3. The attempt at a solution
    it said "Follows from previous item, and B=T×N". I simply don't see how it follows, though.
     
  2. jcsd
  3. Jul 20, 2014 #2

    pasmith

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    Homework Helper

    You know that [itex]\frac{d\mathbf{N}}{ds}[/itex] must be orthogonal to [itex]\mathbf{N}[/itex]. Hence [itex]\frac{d\mathbf{N}}{ds} = C\mathbf{T} + D\mathbf{B}[/itex] for some [itex]C(s)[/itex] and [itex]D(s)[/itex]. You have shown that [itex]C = -\kappa[/itex]. How do you think you should go about finding [itex]D[/itex]?
     
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