Some Aspects of Research on Mechanics of Thin Elastic Rod

Some aspects of research wok on the mechanics of thin elastic rod based on Kirchhoff-Cosserat's model were summarized. The analytical mechanics with arc-coordinate s and time t as double variables was established to formulate the motion of elastic rod. In stability analysis the difference and relationship between Lyapunov's stability and Euler's stability were discussed. The first approximate stability was determined by the characteristic equation with double eigenvalues in different domains, one of which can be determined by geometric conditions in static analysis. The Lyapunov's and Euler's stability conditions of the rod in space domain are the necessary conditions of Lyapunov's stability in time domain. As applications of the Kirchhoff's rod in molecular biology, the explanations of nucleosome structure and the chromosome coiling of DNA were given. Concerning the application in engineering the shape of a hanging rod under gravity and the coiling and stretching process of an extendable space mast were discussed. The motion of an axial moving beam with constant velocity and axial extensive force was discussed as an example of exact Cosserat's rod, the special case of small deformation is the Timoshenko's beam.