Tilted excitation implies odd periodic resonances

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

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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 languageEnglish
Article number012202
Pages (from-to)1-6
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number1
Publication statusPublished - 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.


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


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