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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 Resource. https://mathworld.wolfram.com/ParabolaInvolute.html

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