The equation of motion of a body moving along a vertically hanging cable by deploying the cable from the body or retrieving the cable in the body is derived. The derivation of the equation is given both by means of balance principles and a variational principle. Due to the fact that this system is not conservative the derivation by means of the variational principle requires the introduction of the Carnot energy loss concept. Its explanation is the main objective of this paper. The motion of the free falling folded string and a horizontally moving folded string modelling a whip are treated as examples.
On Balance and Variational Formulations of the Equation of Motion of a Body Deploying Along a Cable
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Crellin, E. B., Janssens, F., Poelaert, D., Steiner, W., and Troger, H. (June 1, 1997). "On Balance and Variational Formulations of the Equation of Motion of a Body Deploying Along a Cable." ASME. J. Appl. Mech. June 1997; 64(2): 369–374. https://doi.org/10.1115/1.2787316
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