THE CRITICAL POINTS OF THE ELASTIC ENERGY AMONG

In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inflection points.

Automated summary

In this research, curves minimizing elastic energy under fixed length and pinned ends are identified using the shooting method. The critical points are found to be wavelike elasticae, and the minimizers are shown to have no loops or interior inflection points.