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Math Help - Curvature (2nd)

  1. #1
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    Curvature (2nd)

    Find the curvature at the following point and then sketch this curve.

    r(t) = <cos(2t), 2*sin(2t), 4t>, t = 0, t = Pi/2

    Note: r is a vector
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  2. #2
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    Hello, Ideasman!

    Where is your difficulty?
    If you have the formula for curvature, go for it!

    This is a very unpleasant problem (especially without LaTeX)
    . . I'll start it off for you.


    Find the curvature at the following point and then sketch this curve.

    . . r(t) .= .< cos(2t), 2Ěsin(2t), 4t >, . at t = 0, t = π/2

    . . . . . . . . . . . . . . . . . . .| v x a |
    Curvature Formula: . k .= .----------
    . . . . . . . . . . . . . . . . . . . . |v|│

    Given: .r(t) .= .< cos(2t), 2Ěsin(2t), 4t >

    Then: .v(t) .= .< -2Ěsin(2t), 4Ěcos(2t), 4 >

    Then: .a(t) .= .< -4Ěcos(2t), -8Ěsin(2t), 0 >

    We will need:

    Code:
                  |     i            j         k |
    | v x a |  =  | -2Ěsin(2t)    4Ěcos(2t)    4 |
                  | -4Ěcos(2t)   -8Ěsin(2t)    0 |

    We also need |v|│ ._________________________
    . . . where |v| .= .√4Ěsin▓(2t) + 16Ěcos▓(2t) + 16

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