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Math Help - 3D Curve Length

  1. #1
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    3D Curve Length

    Can anyone help me calculate the length of a 3D curve? I need to know the length from 0 degrees to 800 degrees of a curve in the form:

    x(t)=(R-r)cos(t)+rcos(((R-r)/R)t)
    y(t)=(R-r)sin(t)-rsin(((R-r)/R)t)
    z(t)=at

    I have specific values that I am using for R, r, and a. The curve is called a Hypocycloid.
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  2. #2
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    Quote Originally Posted by CrashDummy11 View Post
    Can anyone help me calculate the length of a 3D curve? I need to know the length from 0 degrees to 800 degrees of a curve in the form:

    x(t)=(R-r)cos(t)+rcos(((R-r)/R)t)
    y(t)=(R-r)sin(t)-rsin(((R-r)/R)t)
    z(t)=at

    I have specific values that I am using for R, r, and a. The curve is called a Hypocycloid.
    For any curve given by x(t), y(t), and z(t), the arclength is given by \int_{t_0}^{t_1} \sqrt{(x')^2+ (y')^2+ (z')^2}dt.
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  3. #3
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    I tried that but everytime I tried to evaluate the integral for an interval beyond 0-1 it came up as invalid. Any ideas?
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