Explicit parameterization of Euler’s elastica. (English) Zbl 1196.53004
Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 175-186 (2008).
The authors deal with the dynamic system modeling of a novel explicit parametrization of Euler’s elastica. It has the form of a system of nonlinear coupled ordinary differential equations
The solution is expressed using the complete elliptic integral of the first kind. A geometrical and mechanical analysis of the solution is performed.
|53A04||Curves in Euclidean space|