The analytical reduction of the Kirchhoff thin elastic rod model with asymmetric cross section

Abstract

The Kirchhoff thin elastic rod models and related systems are always the important basis to research the topology and stability of the flexible structures in not only the macroscopic but also microscopic scale. Firstly the initial Kirchhoff equations are rebuilt in a complex style to suit the character of obvious asymmetry embodied on the cross section by considering the mathematical background of DNA double helix. Then we introduce a complex form variable solution of the torque, and extend the knowledge of effective bending coefficients as well as its facility in the high dimensional system by using the complicated system. As the result, a simplified second order ordinary differential equation with single variable is obtained. Furthermore the periodically varying bending coefficients of the DNA molecular are considered as the appended components to the effective bending coefficients. The whole reduction process makes the numerical simulation become not solely the exclusively eligible approach, and produces adaptable channel to quantitative analysis.