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EnglishWe consider a natural Lagrangian system and show that from a point $q_0$ in n-space, where the potential energy $V$ has a (weak) maximum, one can go near the boundary of any compact ball where $V(q)\le V(q_0)$ with (arbitrarily small) nonvanishing initial speeds. The result holds true for sets which are $C^2$-diffeomorphic to a compact ball. This property is found as a simple consequence of the Hopf-Rinow theorem and of a theorem of Gordon. As a corollary we deduce a well known local result, namely a `converse' of the Lagrange-Dirichlet theorem, thus obtained via geometric arguments.
| Titolo: | How far can one move from a potential peak with small initial speed? | |
| Autori: | ||
| Data di pubblicazione: | 1994 | |
| Rivista: | ||
| Abstract: | We consider a natural Lagrangian system and show that from a point $q_0$ in n-space, where the potential energy $V$ has a (weak) maximum, one can go near the boundary of any compact ball where $V(q)\le V(q_0)$ with (arbitrarily small) nonvanishing initial speeds. The result holds true for sets which are $C^2$-diffeomorphic to a compact ball. This property is found as a simple consequence of the Hopf-Rinow theorem and of a theorem of Gordon. As a corollary we deduce a well known local result, namely a `converse' of the Lagrange-Dirichlet theorem, thus obtained via geometric arguments. | |
| Handle: | http://hdl.handle.net/11562/393336 | |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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