Dynamics of Stiff Chains. I. Equation of Motion

Starting from a discrete bead model and transforming it into a continuous model, a Lagrangian of a stiff chain of variable length is obtained, where not only the bending but also the stretching freedom is taken into account. By applying the Hamilton's principle to it, a nonlinear equation of motion and free-and boundary conditions that determine the motion of stiff chains in solution are obtained. The physical implication of it is examined and its correctness is clarified. The cause of defects in the conventional equation used by other authors is discussed in comparison with the present equation.