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Swallowtail Catastrophe

Swallowtail
SwallowtailCatastrophe2

A swallowtail catastrophe is a catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension 3, i.e., in three unfolding parameters, and is of the form F(x,u,v,w)=x^5+ux^3+vx^2+wx. The equations

x=uv^2+3v^4
(1)
y=-2uv-4v^3
(2)
z=u
(3)

display such a catastrophe (von Seggern 1993, Nordstrand). The above surface uses u in [-2,2] and v in [-0.8,0.8].

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References

Nordstrand, T. "Swallowtail." http://jalape.no/math/stltxt.htm.Sanns, W. Catastrophe Theory with Mathematica: A Geometric Approach. Germany: DAV, 2000.von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 94, 1993.

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Swallowtail Catastrophe

Cite this as:

Weisstein, Eric W. "Swallowtail Catastrophe." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SwallowtailCatastrophe.html

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