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Closed generalized elastic curves in S2(1)

✍ Scribed by J. Arroyo; O.J. Garay; J.J. Mencı́a


Book ID
104343231
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
334 KB
Volume
48
Category
Article
ISSN
0393-0440

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✦ Synopsis


We study the existence and stability of (closed) curves in S 2 (1) which are critical points of generic curvature energy functionals. Firstly, we compute the first and second variation formulas and obtain first integrals of the Euler-Lagrange equations, then we establish conditions under which critical points close up. We apply the results to analyze two concrete situations: a natural generalization of the classical Euler-Bernoulli elastic functional and a constrained version of the total curvature functional.


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