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Research Article | Open Access

Timoshenko beam under finite and dynamic transformations: Lagrangian coordinates and Hamiltonian structures

Oscar Cosserat1( ), Loïc Le Marrec2
Georg-August-University Göttingen, Bunsenstraße 3-5, 37073, Göttingen, Germany
Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
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Abstract

In the framework of Timoshenko beam, the material parameters were inherently prescribed on the material moving frame. In this regard, we derived the strong and weak formulations of the dynamics under finite transformation in Lagrangian coordinates. Accordingly, analytical mechanics tools were used to deduce a new Hamiltonian formulation of the model which proved to be remarkably simple and synthetic.

Keywords

Timoshenko beamgeometrically exact formulationlarge transformationLagrangian coordinatesHamiltonian mechanicsPoisson brackets
CLC number: 35F20, 74K10, 37K58

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Communications in Analysis and Mechanics
Volume 18 Issue 1,
March 2026
Pages 37-69
DOI: 10.3934/cam.2026002

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Cite this article:
Cosserat O, Le Marrec L. Timoshenko beam under finite and dynamic transformations: Lagrangian coordinates and Hamiltonian structures. Communications in Analysis and Mechanics, 2026, 18(1): 37-69. https://doi.org/10.3934/cam.2026002

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Received: 03 April 2025
Revised: 25 September 2025
Accepted: 26 September 2025
Published: 12 January 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)