  A new method is proposed for integrating the equations of motion of an
elastic filament. In the standard finite-difference and finite-element
formulations the continuum equations of motion are discretized in space and
time, but it is then difficult to ensure that the Hamiltonian structure of the
exact equations is preserved. Here we discretize the Hamiltonian itself,
expressed as a line integral over the contour of the filament. This discrete
representation of the continuum filament can then be integrated by one of the
explicit symplectic integrators frequently used in molecular dynamics. The
model systematically approximates the continuum partial differential equations,
but has the same level of computational complexity as molecular dynamics and is
constraint free. Numerical tests show that the algorithm is much more stable
than a finite-difference formulation and can be used for high aspect ratio
filaments, such as actin.
