Tilted excitation implies odd periodic resonances

G. I. Depetri; J .C. Sartorelli; B. Marin; M. S. Baptista

doi:10.1103/PhysRevE.94.012202

Tilted excitation implies odd periodic resonances

G. I. Depetri, J .C. Sartorelli, B. Marin, M. S. Baptista

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Abstract

Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case.

Original language	English
Article number	012202
Pages (from-to)	1-6
Number of pages	6
Journal	Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume	94
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevE.94.012202
Publication status	Published - 5 Jul 2016

Bibliographical note

This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions.

Keywords

parametric pendulum
parametric resonances
sub-harmonic resonances
Melnikov method
numeric continuation

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title = "Tilted excitation implies odd periodic resonances",

abstract = "Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case. ",

keywords = "parametric pendulum, parametric resonances, sub-harmonic resonances, Melnikov method, numeric continuation",

author = "Depetri, {G. I.} and Sartorelli, {J .C.} and B. Marin and Baptista, {M. S.}",

note = "This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions. ",

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AU - Depetri, G. I.

AU - Sartorelli, J .C.

AU - Marin, B.

AU - Baptista, M. S.

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N2 - Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case.

AB - Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case.

KW - parametric pendulum

KW - parametric resonances

KW - sub-harmonic resonances

KW - Melnikov method

KW - numeric continuation

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Tilted excitation implies odd periodic resonances

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