Archivio Istituzionale della RicercaWe study critical trajectories in the sphere for the 1/2-Bernoulli’s bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of infinitely many closed trajectories which depend on a pair of relatively prime natural numbers. A geometric description of these numbers and the relation with the shape of the corresponding critical trajectories is also given.
Closed 1/2-Elasticae in the 2-Sphere / Musso, Emilio; Pámpano, Álvaro. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - ELETTRONICO. - 33:1(2022), pp. 1-48. [10.1007/s00332-022-09860-3]
Closed 1/2-Elasticae in the 2-Sphere
Musso, Emilio;
2022
Abstract
We study critical trajectories in the sphere for the 1/2-Bernoulli’s bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of infinitely many closed trajectories which depend on a pair of relatively prime natural numbers. A geometric description of these numbers and the relation with the shape of the corresponding critical trajectories is also given.
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NonLinearScience22:23.pdf
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https://hdl.handle.net/11583/2972651