2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156728Time-dependent Hamiltonian dynamics is derived for a curve (molecular strand) in $\mathbb{R}^3$ that experiences both nonlocal (for example, electrostatic) and elastic interactions. The dynamical equations in the symmetry-reduced variables are written on the dual of the semidirect-product Lie algebra $so(3) \circledS (\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3)$ with three 2-cocycles. We also demonstrate that the nonlocal interaction produces an interesting new term deriving from the coadjoint action of the Lie group SO(3) on its Lie algebra $so(3)$. The new filament equations are written in conservative form by using the corresponding coadjoint actions.6 pages, 1 figure, 13 references. Submitted to Compte Rendus Acad Sci. Paris, MathAdaptation and Self-Organizing SystemsPattern Formation and Solitonstext