Book chapter
Elastica and Minimal–Energy Splines
Curves and Surfaces, pp.247-250
Elsevier Inc
1991
DOI: 10.1016/B978-0-12-438660-0.50037-6
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.
Details
- Title: Subtitle
- Elastica and Minimal–Energy Splines
- Creators
- Emery JouWeimin Han
- Resource Type
- Book chapter
- Publication Details
- Curves and Surfaces, pp.247-250
- DOI
- 10.1016/B978-0-12-438660-0.50037-6
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 1991
- Academic Unit
- Mathematics
- Record Identifier
- 9984242447702771
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