The Tallest Column -- A Dynamical System Approach using a Similarity Solution

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dc.creatorFarjoun, Yossi
dc.creatorNeu, John C.
dc.date2007-11-05
dc.date2008-01-21
dc.date.accessioned2026-07-07T08:55:13Z
dc.date.available2026-07-07T08:55:13Z
dc.descriptionA classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the direction of the stable manifold, and solving backwards numerically. This removes the need for an iterative integration method that was previously used. The method is shown to work for clamped or hinged boundary condition and can also be used for other problems involving singularities at the endpoints.
dc.description18 pages, 5 figures; typo in title fixed
dc.identifierhttps://arxiv.org/abs/0711.0730
dc.identifierhttp://arxiv.org/abs/0711.0730
dc.identifierStudies in Applied Math (115) 319--337, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146205
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.titleThe Tallest Column -- A Dynamical System Approach using a Similarity Solution
dc.typetext

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