Poinsot's spirals

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In mathematics, Poinsot's spirals are two spirals represented by the polar equations

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure, space, and change.

Spiral curve which emanates from a point, moving farther away as it revolves around the point

In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.

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where csch is the hyperbolic cosecant, and sech is the hyperbolic secant. [1] They are named after the French mathematician Louis Poinsot.

Louis Poinsot French mathematician and physicist

Louis Poinsot was a French mathematician and physicist. Poinsot was the inventor of geometrical mechanics, showing how a system of forces acting on a rigid body could be resolved into a single force and a couple.

Examples of the two types of Poinsot's spirals

The Poinsot spiral r=csch(th/3). Poinsot2.svg
The Poinsot spiral r=csch(θ/3).
The Poinsot spiral r=sech(th/3). Poinsot1.svg
The Poinsot spiral r=sech(θ/3).

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References

  1. Lawrence, J. Dennis (1972). A Catalog of Special Plane Curves. New York: Dover. pp. 192–194. ISBN   0486602885.