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Elastica and Minimal–Energy Splines
Book chapter

Elastica and Minimal–Energy Splines

Emery Jou and Weimin Han
Curves and Surfaces, pp.247-250
Elsevier Inc
1991
DOI: 10.1016/B978-0-12-438660-0.50037-6

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Abstract

When the end-points of an elastica of fixed length is clamped or supported, the elastica assumes a shape such that the strain energy is minimized. The strain energy of an elastica is proportional to the integral of the square of curvature taken along the elastica. A curve obtained by minimizing the strain energy is called a minimal-energy spline. A minimal-energy spline has a prescribed length together with the constraints of arbitrary-angles or zero-curvatures at the end-points. The minimal-energy splines are curvature continuous curves. Each segment of a minimal-energy spline is infinitely smooth and has linear curvature relationship.

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