A Lax Pair for the Dynamics of DNA Modeled as a Shearable and Extensible Elastic Rod: II. Discretization of the Arc Length

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.