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Displacement of a rigid rod in a viscous medium

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Abstract

The spatial displacement of an absolutely rigid vertical rod in a viscous medium is considered; the rod is hinged at the upper end to a platform moving on the surface of the viscous medium over a specified curvilinear trajectory. A load is attached to the lower end of the rod. Using a variational Lagrangian equation, a nonlinear system of ordinary differential equations in terms of the angles of rod rotation determining the position of points of this rod at any time is obtained. As an example, the problem is solved for conditions of acceleration, uniform motion, and deceleration of the reference point moving over a trajectory consisting of rectilinear sections and portions of circles. The differential equations obtained may be used in determining the position of rod-type elements suspended in a viscous medium.

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References

  1. S. I. Devnin, Aerodynamic Calculation of Poorly Streamlined Ship Designs [in Russian], Leningrad (1967).

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  3. F. L. Shevchenko, Z. E. Filer, and Yu. L. Vetryak, "Displacement of hinged rod in viscous medium with referencepoint motion," Probl. Mashinostr., No. 28, 51–55 (1987).

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Authors
  1. F. L. Shevchenko
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  2. Z. E. Filer
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  3. V. S. Pashchenko
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  4. L. A. Solodova
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Additional information

Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 108–112, 1990.

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Shevchenko, F.L., Filer, Z.E., Pashchenko, V.S. et al. Displacement of a rigid rod in a viscous medium. J Math Sci 68, 718–721 (1994). https://doi.org/10.1007/BF01249414

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  • DOI: https://doi.org/10.1007/BF01249414

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