Helicoseir as Shape of a Rotating String (I): 2D Theory and Simulation Using ANCF

A physically simple but mathematically cumbersome problem of rotating heavy string with one fixed top point was studied. A nonlinear equation of its two-dimensional shapes of relative equilibrium was obtained and solved numerically. A linear case of small displacements was analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of a bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions were studied with the help of a simulation using the absolute nodal coordinate formulation (ANCF); the equilibriums were found to be instable. The reason for instability is explained using a variational principle. The outlines for further full three-dimensional analysis are briefly proposed in this paper, and the full derivation will be explained in the next paper.