Nonlocal orientation-dependent dynamics of molecular strands

Time-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.