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Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation

M. Ferretti () and A. Luongo ()

Advances in Mathematical Physics, 2019, vol. 2019, 1-9

Abstract: The problem of a massive taut string, traveled by a heavy point mass, moving with an assigned law, is formulated in a linear context. Displacements are assumed to be transverse, and the dynamic tension is neglected. The equations governing the moving boundary problem are derived via a variational principle, in which the geometric compatibility between the point mass and the string is enforced via a Lagrange multiplier, having the meaning of transverse reactive force. The equations are rearranged in the form of a unique Volterra integral equation in the reactive force, which is solved numerically. A classical Galerkin solution is implemented for comparison. Numerical results throw light on the physics of the phenomenon and confirm the effectiveness of the algorithm.

Date: 2019
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DOI: 10.1155/2019/6915629

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