Definition:Cornu Spiral
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Definition
The Cornu spiral is the locus $C$ of the equation expressed in intrinsic coordinates as:
- $s = a^2 \kappa$
where:
- $s$ denotes the length of arc at a point of $C$ from the origin
- $\kappa$ denotes the curvature of $C$ at that point.
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Also presented as
The Cornu spiral can also be presented in the form:
- $s = a^2 \dfrac {\d \psi} {\d s}$
where $\psi$ is the turning angle of $C$ at the point where the length of arc from the origin is $s$.
Also known as
Other names for the Cornu spiral include:
- Euler spiral (for Leonhard Paul Euler)
- klothoid or clothoid
Also see
- Results about the Cornu spiral can be found here.
Source of Name
This entry was named for Marie Alfred Cornu.
Historical Note
The Cornu spiral is used primarily for:
- analysis of intensities of diffraction patterns
- designing curves on railway lines and roller coasters so as to provide a smooth curvature transition
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cornu spiral
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): spiral
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cornu spiral
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spiral