Metodi variazionali globali su vincoli non olonomi
The brachistochrone problem with frictional forces
The brachistochrone problem with frictional forces
In this paper we show the existence of the solution for the classical brachistochrone problem under the action of a conservative field in presence of frictional forces. Assuming that the frictional forces and the potential grow at most linearly, we prove the existence of a minimizer on the travel time between any two given points, whenever the initial velocity is great enough. We also prove the uniqueness of the minimizer whenever the given points are sufficiently close.
Buchi neri e singolarità nude
La teoria della Relativita Generale prevede la formazione di singolarita spazio-temporali, delle quali non si conosce ancora la natura. In particolare, non è chiaro se le singolarità che si formano sono sempre inaccessibili da osservatori lontani (sono cioè buchi neri) oppure no. Nell'articolo si discute la situazione attuale delle conoscenze su questo problema, di importanza chiave per la comprensione del collasso gravitazionale.
On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
Let be a complete Riemannian manifold, an open subset whose closure is diffeomorphic to an annulus. If is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in starting orthogonally to one connected component of and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating...
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