I have an equation for a curve that lies along the surface of a truncated cone. In polar coordinates:(adsbygoogle = window.adsbygoogle || []).push({});

theta(r) = K * [ U + arctan(1/U) - (Pi/2) ]

where:

U = SQRT[ ((r/r1)^2) - 1 ]

K = SQRT[ 1 + (H/(r2-r1))^2 ]

r = r1 + (r2-r1)(z/H)

r1 = minor radius of the truncated cone

r2 = major radius of the truncated cone

H = the height of the truncated cone

Physically, think of this as a string wrapped around the truncated cone from one end to the other, with its "angle of attack" varying along the height of the cone.

How can I go about calculating the radius of curvature of this 3D curve as a function of some parameter (preferably arc length)?

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# Radius of Curvature in 3 Dimensions

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