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Problem involving tangent vector, normal vector, binormal vector and curvature

  1. Jul 15, 2012 #1
    1. The problem statement, all variables and given/known data


    r(t)=cos(t)i+sin(t)j+sin(2t)k

    Find the curvature κ, the unit tangent vector T, the principal normal vector N and the binormal vector B at t=0. Find the tangential and normal components of the acceleration at t=∏/4

    2. Relevant equations
    T(t)=r'(t)/|r'(t)|

    N(t)=T'(t)/|T't|

    B(t)=T(t)xN(t)

    κ=|(dT/ds|=|T'(t)|/|r'(t)|=|r'(t)xr''(t)|/|r'(t)|^3



    3. The attempt at a solution

    I have tried every formula and attempted using double angle formulas and keep getting extremely messy and expressions that are getting too big and unwieldy to make sense. I've looked through my book repeatedly and tried using wolfram alpha and every resource I could think of and cannot find anything that covers how to handle only one trig function having a coefficient like that.

    So I'm at a loss and after spending 4 hours on this I'm just frustrated to the point of burn out and just need help getting started or seeing what I'm missing to make this work. Part of me is hoping that it's a typo while the other part will rage.

    So I don't know, I'm going to go cry in a corner now, thank you.
     
  2. jcsd
  3. Jul 16, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, the derivative of T is a bit complicated but that is the only complicated part and it is only that- complicated, not impossible. I don't understand why you have not at least shown the work you have done. What did you get for T? What did you get for [itex]\kappa[/itex]?
     
  4. Jul 16, 2012 #3
    Yes, I e-mailed my professor later after posting this and asked him if I was on the right track, to which he said yes.

    I just felt I was doing something wrong since the expression just kept exploding and I've begun to associate that with me making a careless mistake somewhere. I'd tell you what I got but I had to turn it in this morning, but I think it all turned out. Thanks for the help though. :smile:
     
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