arXiv subjects
Publications and source records attributed to J. E. Hearst.
We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III of a series.
In previous work, the dynamics of the elastic rod was recast in a Lax pair formulation, with fiducial arc length s and time t as continuous independent variables. However, the solution of these equations cannot apply directly to a system where the fiducial arc length s is a discrete variable. In this paper, we show how to discretize the continuous s variable in a way that preserves the integrability of the original system. The t parameter is not discretized, so this algorithm will be especially useful for solutions of the s-discrete and t-continuous elastic rod problem, as may occur in problems where the polymeric structure of the DNA is made explicit.
We introduce a spectral parameter into the geometrically exact Hamiltonian equations for the elastic rod in a way that creates a Lax pair. This assures integrability and permits application of the inverse scattering transform solution method. If the method can be carried through, the solution of the original problem is recovered by setting the spectral parameter to zero.