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            <funder>Mr. Hariz conduced this work within the France 2030 framework programme, the Centre Henri Lebesgue ANR-11-LABX-0020-01.The authors thank the GDR CNRS 2043 GDM (Géométrie Différentielle et Mécanique) for its stimulating research programs and support.</funder>
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              <p>This article presents a formulation for one-dimensional structures. The study employs the Lie group structure and associated differential calculations to describe deformations and dynamic equation of the structure. Three levels of equation setting are explored: level one is the most abstract where a single equation is obtained using the Lie algebra of the displacement group, level two refers to the decomposition of the displacement group into rotation and translation groups as semi-direct product, and the third level is obtained by selecting a suitable basis within the Lie algebra which leads to scalar equations. Equations at each level are derived, and a detailed comparison with the literature is given for the static equilibrium.The article also addresses the dynamic superposition of a static problem with large transformations, providing a perturbation of linear dynamic around an arbitrary equilibrium position. Weak formulation of the dynamic problem is discussed. Symmetry of deformation operator is examined, which has implications for studying instability issues.The results presented in this approach are applicable to any geometrical model and boundary conditions. Further explorations in these fields are left for the future work.</p>
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