Elastica
The elastica 
formed by bent rods and considered in physics can be generalized to curvesin a Riemannian Manifold which are a Critical Point for
where
is the Geodesic Curvature of 
, 
is a Real Number, and is closed orsatisfies some specified boundary condition. The curvature of an elastica must satisfy
where
is the signed curvature of , 
is the Gaussian Curvature of the oriented Riemanniansurface 
along , 
is the second derivative of with respect to 
, and is a constant.
References
Barros, M. and Garay, O. J. ``Free Elastic Parallels in a Surface of Revolution.'' Amer. Math. Monthly 103, 149-156, 1996. Bryant, R. and Griffiths, P. ``Reduction for Constrained Variational Problems and Langer, J. and Singer, D. A. ``Knotted Elastic Curves in Langer, J. and Singer, D. A. ``The Total Squared of Closed Curves.'' J. Diff. Geom. 20, 1-22, 1984.
.'' Amer. J. Math. 108, 525-570, 1986.
.'' J. London Math. Soc. 30, 512-520, 1984.
- Trigonometry Values Pi/16
- Trigonometry Values Pi/17
- Trigonometry Values Pi/18
- Trigonometry Values Pi/2
- Trigonometry Values Pi/20
- Trigonometry Values Pi/3
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- Cyclic Graph
- Cyclic Group
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- Cyclic-Inscriptable Quadrilateral
- Cyclic Number
- Cyclic Pentagon
- Cyclic Permutation
- Cyclic Polygon
- Cyclic Quadrangle
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- Cyclic Redundancy Check
- Cyclid
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- Cyclidic Coordinates
- Cycloid