Tricomi's Φ-equation

We study an autonomous nonlinear differential equation that models the movement of a damped F-pendulum with constant forcing. In the dissipative case, two results are presented, on the one hand, using the application of Poincaré and energy functions, a sufficient criterion is established to guarante...

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Autores:
Castro G., Diego A.
Gutiérrez G., Alexander
Tipo de recurso:
Fecha de publicación:
2018
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
spa
OAI Identifier:
oai:repository.eafit.edu.co:10784/13189
Acceso en línea:
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903
http://hdl.handle.net/10784/13189
Palabra clave:
Periodic solutions
Attractors
Stability
Soluciones periódicas
Atractores
Estabilidad
Rights
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Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G.
Description
Summary:We study an autonomous nonlinear differential equation that models the movement of a damped F-pendulum with constant forcing. In the dissipative case, two results are presented, on the one hand, using the application of Poincaré and energy functions, a sufficient criterion is established to guarantee the existence, uniqueness and asymptotic stability of a periodic solution of the second kind and on the other hand, a criterion is presented with which the basin of attraction of an asymptotically stable equilibrium is estimated analytically with the help of the Lasalle’s invariance principle. While in the conservative case there are necessary conditions for range of the period function to be defined in an unbounded interval. The results obtained in the dissipative case are a generalization of those established by Tricomi in the newtonian case.