Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation. (7th April 2019)

• Record Type: Journal Article
• Authors: Ferretti, M.; Luongo, A.
• Other Names: Turco Emilio Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2019(2019)
• Publication Date: 2019-04-07
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2019/6915629
• Languages: English
• ISSNs: 1687-9120

Abstract

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.