Generic Euler's Elastica
Euler's elastica are stationary profiles of a homogeneous elastic rod with fixed endpoint locations and tangents. This Demonstration provides a tool for plotting and evaluating generic Euler's elastica. Mathematically, the problem on finding elastica can be stated as follows: Let an elastic rod in have a fixed length . Take any points and arbitrary unit tangent vectors at these points . The problem consists of finding the profile of a rod , starting at the point and ending at the point with the corresponding tangent vectors and and with the minimum elastic energy. We can replace the vectors by the angles between the vectors and axis . So the problem is stated in the space . There are five types of Euler's elastica: inflectional, non-inflectional, critical, circular, and linear. This interface plots generic elastica (inflectional and non-inflectional ones) and evaluates their parametrization in terms of Jacobi's elliptic functions.
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"Generic Euler's Elastica"
Wolfram Demonstrations Project
Published: December 5 2012