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
• DOI: 10.1016/s0393-0440(03)00047-0

✦ 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.