Geometry of the free-sliding Bernoulli beam. (English) Zbl 1397.58006

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.


58E30 Variational principles in infinite-dimensional spaces
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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