On the Question of Nonlinear Fluctuations of Heavy Ropes

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Abstract: Due to the methods of the dynamics of curvilinear motion the system of nonlinear differential equations describing two-dimensional arbitrary displacements of a heavy rope, one end of which is free, and the other is fastened is obtained. The problem is solved in the language of displacement vector ()()(),,,xyxtxtxtξξξ=+ij, where (),xxtξ and (),yxtξ accordingly, arbitrary offsets of the rope points in the axes of coordinates. It is shown that in the limit of small oscillations the obtained equations are reduced to the description of the weak offsets of the horizontal string fixed on both ends, and small displacements of the heavy vertical filament, fluctuating due to the force of gravity. The main goal of the paper is the mathematical description of the strong non-equilibrium dynamic systems.

WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 15, 2020, Art. #4

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Sergey O. Gladkov, "On the Question of Nonlinear Fluctuations of Heavy Ropes," WSEAS Transactions on Applied and Theoretical Mechanics, vol. 15, pp. 24-30, 2020, DOI:10.37394/232011.2020.15.4
Sergey O. Gladkov. On the Question of Nonlinear Fluctuations of Heavy Ropes. WSEAS Transactions on Applied and Theoretical Mechanics. 2020;15:24-30. 10.37394/232011.2020.15.4
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