By using Pontryagin’s maximum principle we determine the shape of the lightest rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. Three variational principles for this boundary value problem are formulated and a first integral is constructed. The optimal shape of a rod is determined by numerical integration.
On the Optimal Shape of a Rotating Rod
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, September 26, 2000; final revision, April 15, 2001. Associate Editor: N. C. Perkins. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Atanackovic, T. M. (April 15, 2001). "On the Optimal Shape of a Rotating Rod ." ASME. J. Appl. Mech. November 2001; 68(6): 860–864. https://doi.org/10.1115/1.1409938
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