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Helicoseir as Shape of a Rotating String (I): 2D Theory and Simulation Using ANCF

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Abstract

A physically simple but mathematically cumbersome problem of rotating heavy string with one fixed top point was studied. A nonlinear equation of its two-dimensional shapes of relative equilibrium was obtained and solved numerically. A linear case of small displacements was analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of a bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions were studied with the help of a simulation using the absolute nodal coordinate formulation (ANCF); the equilibriums were found to be instable. The reason for instability is explained using a variational principle. The outlines for further full three-dimensional analysis are briefly proposed in this paper, and the full derivation will be explained in the next paper.

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Authors and Affiliations

  1. National Research Laboratory of CAE, Pusan National University, Busan, Korea

    Oleg Dmitrochenko (Post-doctoral researcher)

  2. National Research Laboratory of CAE, Pusan National University, Busan, Korea

    WanSuk Yoo (Professor, Director)

  3. Department of Applied Mechanics, Bryansk State Technical University, Bryansk, Russia

    Dmitry Pogorelov (Professor)

Authors
  1. Oleg Dmitrochenko
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  2. WanSuk Yoo
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  3. Dmitry Pogorelov
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Correspondence to Oleg Dmitrochenko.

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Dmitrochenko, O., Yoo, W. & Pogorelov, D. Helicoseir as Shape of a Rotating String (I): 2D Theory and Simulation Using ANCF. Multibody Syst Dyn 15, 135–158 (2006). https://doi.org/10.1007/s11044-005-9002-2

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  • DOI: https://doi.org/10.1007/s11044-005-9002-2

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