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Parabola Involute

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ParabolaInvolute

The involute of a parabola

x=at^2
(1)
y=at
(2)

is given by

x_i=-(atsinh^(-1)(2t))/(2sqrt(4t^2+1))
(3)
y_i=a(1/2t-(sinh^(-1)(2t))/(4sqrt(4t^2+1))).
(4)

Defining t=sinhu/u, this can be written in the slightly simpler form

x_i=-1/4autanhu
(5)
y_i=1/4a(sinhu-usechu).
(6)

See also

Parabola, Parabola Evolute

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Cite this as:

Weisstein, Eric W. "Parabola Involute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParabolaInvolute.html

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