Classification of the Spatial Equilibria of the Clamped Elastica: Symmetries and Zoology of Solutions |
| |
Authors: | Sébastien Neukirch Michael E Henderson |
| |
Institution: | (1) Bernoulli Institute, School of Basic Sciences, école Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;(2) T.J. Watson Research Center I.B.M., Yorktown Heights, NY, 10598, U.S.A. |
| |
Abstract: | We investigate the configurations of twisted elastic rods under applied end loads and clamped boundary conditions. We classify
all the possible equilibrium states of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic
rods. We show that all solutions of the clamped boundary value problem exhibit a π-flip symmetry. The Kirchhoff equations
which describe the equilibria of these rods are integrated in a formal way which enable us to describe the boundary conditions
in terms of 2 closed form equations involving 4 free parameters. We show that the flip symmetry property is equivalent to
a reversibility property of the solutions of the Kirchhoff differential equations. We sort these solutions according to their
period in the phase plane. We show how planar untwisted configurations as well as circularly closed configurations play an
important role in the classification.
This revised version was published online in June 2006 with corrections to the Cover Date. |
| |
Keywords: | classification of boundary value problem solutions for elastic rods |
本文献已被 SpringerLink 等数据库收录! |
|