Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation
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 pr...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/6915629 |
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| _version_ | 1832555519181586432 |
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| author | M. Ferretti A. Luongo |
| author_facet | M. Ferretti A. Luongo |
| author_sort | M. Ferretti |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2c1a8bee981b4b6cac8c3290f5f60727 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2c1a8bee981b4b6cac8c3290f5f607272025-02-03T05:47:55ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/69156296915629Solution to the Problem of a Mass Traveling on a Taut String via Integral EquationM. Ferretti0A. Luongo1International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, 67100 L’Aquila, ItalyInternational Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, 67100 L’Aquila, ItalyThe 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.http://dx.doi.org/10.1155/2019/6915629 |
| spellingShingle | M. Ferretti A. Luongo Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation Advances in Mathematical Physics |
| title | Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation |
| title_full | Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation |
| title_fullStr | Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation |
| title_full_unstemmed | Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation |
| title_short | Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation |
| title_sort | solution to the problem of a mass traveling on a taut string via integral equation |
| url | http://dx.doi.org/10.1155/2019/6915629 |
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