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September 10, 2025MathematicsOpen Access

Elastic Curves and Euler–Bernoulli Constrained Beams from the Perspective of Geometric Algebra

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This exploration shows a unified approach to elastic curves using geometric algebra, revealing key links to Euler-Bernoulli models.

A unified and coordinate-free approach in examining the geometric properties of elastic curves enhances computational efficiency.
The study systematically derives Frenet, Darboux, and Bishop frames, integral to understanding the elastica equation and elasticity theory.
A concise Lagrangian formulation identifies conserved multi-vector moments, illustrating significant structural simplifications in elastic systems.
Insights into classical beam models, including Euler-Bernoulli formulations, are derived as special cases, expanding applications in continuum mechanics.

Dimiter Prodanov (2025) studied this question.

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