The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is characterized as a critical point of the energy functional obtained by adding the effect of twisting to the bending energy. In this paper, we investigate Kirchhoff elastic rods in three-dimensional space forms. In particular, we give explicit formulas of Kirchhoff elastic rods in the three-sphere and in the three-dimensional hyperbolic space in terms of Jacobi sn function and the elliptic integrals.
Publié le : 2008-04-15
Classification:
elastic rod,
elastica,
calculus of variations,
58E10,
74K10,
74G05
@article{1212156662,
author = {KAWAKUBO, Satoshi},
title = {Kirchhoff elastic rods in three-dimensional space forms},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 551-582},
language = {en},
url = {http://dml.mathdoc.fr/item/1212156662}
}
KAWAKUBO, Satoshi. Kirchhoff elastic rods in three-dimensional space forms. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 551-582. http://gdmltest.u-ga.fr/item/1212156662/