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The Tallest Column—A Dynamical System Approach Using a Symmetry Solution
Author(s) -
Farjoun Yossi,
Neu John
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2005.00316.x
Subject(s) - singularity , gravitational singularity , manifold (fluid mechanics) , mathematics , point (geometry) , mathematical analysis , boundary (topology) , work (physics) , boundary value problem , critical point (mathematics) , dynamical system (definition) , symmetry (geometry) , dynamical systems theory , geometry , physics , engineering , mechanical engineering , quantum mechanics , thermodynamics
A 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 backward 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.