Swallowtail Catastrophe (original) (raw)
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A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity 
with codimension 3, i.e., in three unfolding parameters, and is of the form 
. The equations
display such a catastrophe (von Seggern 1993, Nordstrand). The above surface uses ![u in [-2,2]](http://mathworld.wolfram.com/images/equations/SwallowtailCatastrophe/Inline12.svg)
and ![v in [-0.8,0.8]](http://mathworld.wolfram.com/images/equations/SwallowtailCatastrophe/Inline13.svg)
.
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References
Nordstrand, T. "Swallowtail." http://jalape.no/math/stltxt.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.
Cite this as:
Weisstein, Eric W. "Swallowtail Catastrophe." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SwallowtailCatastrophe.html