A quasi-dynamic model and a symplectic algorithm of super slender Kirchhoff rod

Abstract

Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA. The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff rod. In this paper, Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod, then a symplectic algorithm is applied in its numerical simulations. Finally, a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.