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Help with basic multivariable problem.

  1. Sep 17, 2009 #1
    Help with basic multivariable problem. [SOLVED]

    1. The problem statement, all variables and given/known data
    Two surfaces intersect at a space curve C.
    The two surfaces are 4y2 + 9z2 = 36 and x = 2y2 - 3z2

    Find a vector parametrization for C. (r(t) = ( f(t) , g(t) , h(t) )
    Find a set of values for the parameter t over which C is traced once.
    2. Relevant equations

    None needed.

    3. The attempt at a solution
    I've solved for a vector curve r(t) = ( t , [tex]\sqrt{3t/10+36/10}[/tex], [tex]\sqrt{2t/15-36/15}[/tex])

    I used x=t and solved the rest, but I'm not sure that it even correct. Additionally, I have no idea how I will find bounds for exactly one trace of C.
     
    Last edited: Sep 17, 2009
  2. jcsd
  3. Sep 17, 2009 #2

    lanedance

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    Homework Helper

    hi vampire, your paramterisation may not help as i don't think it traces teh whole curve, only a piece of it

    have a think about your two sufaces, maybe try drawing some pieces along the axis planes in 3D...

    The first equation represents a elliptic cylinder along the axis, the 2nd is harder to draw & looks like some kind of saddle type thing...

    However its likely the 2nd surface cuts completely through the cylinder... giving a distorted ellipse over which C will retrace itself

    With this mind... an idea could be to first try and parameterise z & y in terms of the projected ellipse on the y-z plane.

    Choose cylindrical coordinates, with cylinder along the x axis, then z & y should be easy to parameterise in term of the angle. This should solve the first equation, use your 2nd to get x.

    Not 100% it will work, but worth a crack...
     
  4. Sep 17, 2009 #3
    Thank you for your help! Looking at it facing the y-z plane helped me solve it; thank you, lanedance.

    I've solved it. I parametrized the elliptical cylinder using trigonometric functions:

    z= 2sin(t) y= 3cos(t) and solved for x. x= 18cos^2(t) - 12sin^2(t)

    t (0,2[tex]\pi[/tex])
     
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