Elastica as a dynamical system

TL;DR

This paper explores the elastica as a dynamical system derived from the calculus of variations, discussing its properties and potential for quantization.

Contribution

It presents a novel perspective by modeling elastica as a dynamical system and explores its quantization, bridging geometry and quantum theory.

Findings

Elastica can be formulated as a second order variational dynamical system.

The paper discusses the quantization of elastica, linking classical geometry with quantum concepts.

Provides a new framework for understanding elastica through dynamical systems theory.

Abstract

The elastica is a curve in $\R^3$ that is stationary under variations of the integral of the square of the curvature. Elastica is viewed as a dynamical system that arises from the second order calculus of variations, and its quantization is discussed.