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arXiv · 2605.31570

Variational theory of Cosserat arches and affine tensors

Géry de Saxcé
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Abstract

Our purpose is to revisit the screw theory in light of the affine tensor formalism, introducing the co-momentum and momentum tensors. Our target-applications of the Euler-Poincar\'e equation are problems of mechanics such as the motion of the rigid body or the statics and the dynamics of Cosserat arches, in relation to the concept of momentum tensor. Using the framework of Ehresmann connections on the principal bundle of affine frames, we show that the Euler-Poincar\'e equation means that the momentum tensor is parallel-transported.

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Géry de Saxcé. 2026-05-29. Variational theory of Cosserat arches and affine tensors. https://arxiv.org/abs/2605.31570

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