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.

Issue Section:
Technical Papers
Topics:
Cables, Equations of motion, String, Variational principles, Energy dissipation, Modeling
1.
Beletsky, V. V., and Levin, E. M., 1993, “Dynamics of Space Tether Systems,” Advances of the Astronautical Sciences, Vol. 83, AAS Publications, San Diego, CA.
2.
Crellin, E. B., Janssens, F., and Poelaert D., 1995, “Deployment and Retraction of a Continuous Tether—The Equations Revisited,” Proceedings of the Fourth International Conference on Tethers in Space, Science and Technology Corporation, Hampton, VA, pp. 1415–1423.
3.
Hamel, G., 1949, “Theoretische Mechanik,” Grundlehren der Mathematischen Wissenschaften, Vol. 62, Springer-Verlag, Berlin, p. 643.
4.
Kohler, P., Maag, W., Wehrli, R., Weber, R., and Brauchli, H., 1978, “Dynamics of a System of two Satellites Connected by a Deployable and Extensible Tether of Finite Mass,” ESTEC Contract No. 2992/76/NL/AK(SC).
5.
Lur’e, L., 1968, “Me´canique Analytique,” Vols. 1 and 2, Masson &Cie, Paris.
6.
Proceedings of the Fourth International Conference on Tethers in Space, 1995, Science and Technology Corporation, Hampton, VA.
7.
Rosenberg, R., 1991, “Analytical Dynamics of Discrete Systems,” Mathematical Concepts and Methods in Science and Engineering, Vol. 4, third printing, Plenum Press, p. 322.
8.
Schagerl, M., Steindl, A., Steiner, W., and Troger, H., 1997, “On the paradoxon of the free falling folded chain,” Acta Mechanica, in press.
9.
Steiner, W., Steindl, A., and Troger, H., 1995, “Dynamics of a Tethered Satellite System with Two Rigid Endbodies,” Proceedings of the Fourth International Conference on Tethers in Space, Science and Technology Corporation, Hampton, VA, pp. 1367–1379.
10.
Steiner
W.
, and
Troger
H.
,
1995
, “
On the equations of motion of a folded inextensible string
,”
Z. angew. Math. Phys.
, Vol.
46
, pp.
960
–
970
.
11.
Sommerfeld A., 1943, “Vorlesungen u¨ber Theoretische Physik,” Vol. 1: Mechanik, Akademische Verlagsgesellschaft, Leipzig, p. 249.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.