Geodesic
Geometry of the free-sliding Bernoulli beam
Communications in Mathematics, Tome 24 (2016) no. 2, pp. 153-171 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 12X34, 58E30, 74K10
Keywords: Global Analysis; Calculus of Variations; Free Boundary Problems; Jet Spaces; Bernoulli Beam 
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Moreno, Giovanni; Stypa, Monika Ewa. Geometry of the free-sliding Bernoulli beam. Communications in Mathematics, Tome 24 (2016) no. 2, pp. 153-171. http://geodesic.mathdoc.fr/item/COMIM_2016_24_2_a5/

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