Dynamical analysis of stretching process of helical rod to straight rod under constraint of cylinder

The deformation of an elastic helical rod under the unilateral constraint of a cylinder is discussed as a simplified model of the stretching process of an extendable space mast in astronautic technique. The deformation of the rod in stretching process is sufficiently large, and the hypothesis of small deformation can not be applied in analysis. The Kirchhoff's dynamical analogy theory is an effective approach in research of super-large deformation of thin elastic rod. Considering the existence of constraint force of the cylinder the Kirchhoff's equations of a rod without distributed force can not be applied directly, and the distributed constraint force should be added. In present paper the nonlinear differential equations of dynamics of an elastic rod constrained by a cylinder are established with the Euler angles as attitude variables of the cross section. Assume that the rod maintains the helical shape with unchanged radius in the stretching process as the result of cylindrical constraint, and only the variation of pitching angle of helix and the twisting of the rod are considered. Analytical solutions of the simplified differential equations can be obtained to describe the dynamical process of stretching motion, and simple formulas of stretching velocity and stretching time are given in analytical form.