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.Comment: 12 page

Moreno, Giovanni

Stypa, Monika Ewa

English

arXiv

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 the 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 the particular free boundary values variational problem of the free-sliding Bernoulli beam

Episciences.org

Geometry of the free-sliding Bernoulli beam

summary: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 the 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 the particular free boundary values variational problem of the free-sliding Bernoulli beam. This paper is dedicated to the memory of prof. Gennadi Sardanashvily

Institute of Mathematics AS CR, v. v. i.

Abstract
                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 the 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 the particular free boundary values variational problem of the free-sliding Bernoulli beam. </jats:p

Geometry of the free-sliding Bernoulli beam

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Episciences.org

Institute of Mathematics AS CR, v. v. i.

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