ON THE RECIPROCAL OF THE DIRICHLET-LAGRANGE THEOREM

Authors

  • Gerard John Alva Morales

DOI:

https://doi.org/10.17268/sel.mat.2016.02.01

Keywords:

Stability of Lyapunov, Hamiltonian Systems, Dirichlet-Lagrange theorem, Cetaev's theorem

Abstract

We study the instability in Lyapunov's sense of an equilibrium point of a Hamiltonian system with n degrees of freedom for a broad class of potential energies. We will show that this kind of potential energies determine sucient conditions for the instability of this equilibrium point.

References

Gerard John Alva Morales; Estabilidade de Liapunov e derivada radial; Tese de Doutorado, IME-USP, Outubro (2014).

Barone Neto; Jet-detectable Extrema; Proceding A.M.S, (1984).

R.S. Freire Jr., M.V.P. Garcia, F.A. Tal; Instability of equilibrium points of some Lagrangian systems; Journal of Dierential Equations, 245, (2008), 490-504.

Manuel V.P. Garcia, Fabio A. Tal; Stability of equilibrium of conservative systems with two degrees of freedom; Journal of Dierential Equations, 194, (2003), 364-381.

Vinicio Moauro and Piero Negrini; On the Inversion of Lagrange-Dirichlet Theorem; Dierential and Integral Equations,Volume 2, Number 4, October (1989), pp. 471-478.

N. Rouche, P. Habets, M. Laloy; Stability Theory by Liapunovs Direct Method; Springer-Verlag New York, (1977).

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Published

2016-12-11

How to Cite

Alva Morales, G. J. (2016). ON THE RECIPROCAL OF THE DIRICHLET-LAGRANGE THEOREM. Selecciones Matemáticas, 3(02), 67-70. https://doi.org/10.17268/sel.mat.2016.02.01

Issue

Vol. 3 No. 02 (2016): August - December

Section

Articles

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