Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Moreno - Monika Ewa Stypa

Geometry of the free-sliding Bernoulli beam

created by moreno on 15 Sep 2020



Inserted: 15 sep 2020
Last Updated: 15 sep 2020

Year: 2017

ArXiv: 1703.03945 PDF


If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the problem of finding the shortest curve whose endpoints can slide along two prescribed curves. There exists a rigorous geometric way to formulate this sort of problems on smooth manifolds with boundary, which we review here in a friendly self-contained way. As an application, we study a particular free boundary values variational problem, the free-sliding Bernoulli beam.

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