The elastica problem under area constraint
نویسندگان
چکیده
منابع مشابه
Area-constrained planar elastica.
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties; not only can the Euler-Lagrange equation be integrated to provide a quadrature for ...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2015
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-015-1284-y