Variational Study of Nonlinear Spline Curves
Abstract
The paper is an exposition of the variational and differential properties of nonlinear spline curves, based on the Euler-Bernoulli theory for the bending of thin beams or elastica. For both open and closed splines through prescribed nodal points in the Euclidean plane, various types of nodal constraints are considered, and the corresponding algebraic and differential equations relating curvature, angle, arc length, and tangential force are derived in a simple manner. The results for closed splines are apparently new, and they cannot be derived by the consideration of a constrained conservative system. There is a survey of the scanty recent literature.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1971
- Accession Number
- AD0732766
Entities
People
- Erastus H. Lee
- George E. Forsythe
Organizations
- Stanford University