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On the equations of motion of the folded inextensible string

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Abstract

In a number of excellent, even recently published, books in Theoretical Mechanics the equations of motion of a folded inextensible string, for example to explain the crack of a whip, are derived using either the energy principle, if a system of one degree of freedom is considered, or Lagrange's equations for conservative systems, if a system of more than one degree of freedom is studied. However, it will be shown in this paper that the resulting equations are incorrect because physically a nonconservative system is given. Hence, both methods mentioned above based on energy conservation must not be used. A correct derivation of the equations of motion is given by means of the linear momentum balance.

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Authors and Affiliations

  1. Technical University Vienna, A-1040, Vienna, Austria

    W. Steiner & H. Troger

Authors
  1. W. Steiner
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  2. H. Troger
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Steiner, W., Troger, H. On the equations of motion of the folded inextensible string. Z. angew. Math. Phys. 46, 960–970 (1995). https://doi.org/10.1007/BF00917880

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  • DOI: https://doi.org/10.1007/BF00917880

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