Kirchhoff elastic rods in the three-sphere
Kawakubo, Satoshi
Tohoku Math. J. (2), Tome 56 (2004) no. 1, p. 205-235 / Harvested from Project Euclid
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The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is a critical point of the energy functional with the effect of bending and twisting. In this paper, we study Kirchhoff elastic rods in the three-sphere of constant curvature. In particular, we give explicit expressions of Kirchhoff elastic rods in terms of elliptic functions and integrals. In addition, we obtain equivalent conditions for Kirchhoff elastic rods to be closed, and give an example of closed Kirchhoff elastic rods.
Publié le : 2004-06-14
Classification:  Elastic rods,  calculus of variations,  74K10,  58E10,  58E50 
@article{1113246551,
     author = {Kawakubo, Satoshi},
     title = {Kirchhoff elastic rods in the three-sphere},
     journal = {Tohoku Math. J. (2)},
     volume = {56},
     number = {1},
     year = {2004},
     pages = { 205-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1113246551}
}

Kawakubo, Satoshi. Kirchhoff elastic rods in the three-sphere. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp.  205-235. http://gdmltest.u-ga.fr/item/1113246551/