### DYNAMIC BEHAVIOR OF MOVING CHAINS

#### Abstract

We study the dynamic behavior of a three-dimensional chain that is attached at one end both theoretically and numerically. Using the Laplace transform we derive the explicit solution for the linear problem where the chain is initially supported at rest at the horizontal axis and fastened at origin. We present numerical simulations for both linear and the nonlinear problems that confirm earlier experimental findings related to this problem. Introducing Frenet-Serret formulas, we derive an equivalent nonlinear problem that shows interesting relationship between the curvature and the torsion of the chain. Further, we use particular changes of variables to derive two equivalent non- linear problems.

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