Stability of equilibrium of conservative systems with two degrees of freedom |
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Authors: | Manuel V.P. Garcia,Fá bio A. Tal |
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Affiliation: | a Depto. Mat. Aplicada, IME - USP, Brazil b Pós Graduação, Depto. Mat. Aplicada, MAP - IME - USP, Brazil |
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Abstract: | This article intends to study the Liapounof's stability of an equilibrium of conservative Lagrangian systems with two degrees of freedom.We consider an open neighborhood of the origin and the Lagrangian , where of class is the potential energy with a critical point at the origin and is the kinetic energy, of class .We assume that π has a jet of order k at the origin, and this jet shows that the potential energy does not have a minimum in 0. With these hypotheses we prove that (0;0) is an unstable equilibrium according to Liapounof for the Lagrange equations of . We achieve this by proving that there is an asymptotic trajectory to the origin. |
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Keywords: | Liapunof stability Dirichlet-Lagrange Theorem Lagragragian conservative systems |
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