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BIFURCATION BEHAVIOR OF THE FURUTA PENDULUM

Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad Cardenal Herrera-CEU, 46115 Alfara del Patriarca, Spain

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E. FREIRE

Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

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J. GALÁN-VIOQUE

Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

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https://doi.org/10.1142/S0218127407018634Cited by:4 (Source: Crossref)

Abstract

The dynamical behavior of a simple pendulum hanging from a rotating arm has been investigated. The system is invariant under rotations around the axis and can be formulated as a two-degrees of freedom integrable Hamiltonian system in the absence of external forcing. The bifurcation diagram is organized around the relative equilibria (solutions that are invariant under the symmetry) and bridges connecting different bifurcation points. Special attention has been given to those solutions that could shed some light into the stabilization of the upside down solution and the control problem.

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