The Reverse Spaghetti Problem: Drooping Motion of an Elastica Issuing from a Horizontal Guide

[+] Author and Article Information
L. Mansfield, J. G. Simmonds

Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22901

J. Appl. Mech 54(1), 147-150 (Mar 01, 1987) (4 pages) doi:10.1115/1.3172949 History: Received December 11, 1985; Revised May 07, 1986; Online July 21, 2009


The nonlinear equations of motion of an elastica that moves out of a horizontal guide at a constant velocity are expressed in terms a dimensionless weight-to-stiffness ratio and a dimensionless velocity. The equations are written in horizontal-vertical directions rather than tangential-normal directions to minimize algebraic complexities. The introduction of deformation potentials allows each of the linear momentum equations to be integrated once. This simplifies the remaining equations. A series solution of the equations, useful for small motions—and perhaps useful for design—is given. To facilitate numerical solution, the triangular space-time domain of the problem is transformed into a square domain in pseudo space-time. Finally, some solutions based on the finite element method are presented for typical values of the dimensionless weight-to-stiffness and velocity parameters.

Copyright © 1987 by ASME
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