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Catenary Evolute

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CatenaryEvolute

The parametric equations for a catenary are

x=t
(1)
y=acosh(t/a),
(2)

giving the evolute as

x=t-a/2sinh((2t)/a)
(3)
y=2acosh(t/(2a)).
(4)

For t>0, the evolute has arc length function, curvature, and tangential angle given by

s(t)=asinh^2(t/a)
(5)
kappa(t)=(4sqrt(2)sinh(t/a)sinh((2t)/a))/(a[cosh((4t)/a)-1]^(3/2))
(6)
phi(t)=gd(t),
(7)

where gd(t) is the Gudermannian.

See also

Catenary, Catenary Involute, Evolute

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Cite this as:

Weisstein, Eric W. "Catenary Evolute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatenaryEvolute.html

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