Dynamics of a parametrically excited simple pendulum

Autor(es)

Depetri, Gabriela I. ^[1] ; Pereira, Felipe A. C. ^[1] ; Marin, Boris ^[2] ; Baptista, Murilo S. ^[3] ; Sartorelli, J. C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis, Caixa Postal 66318, BR-05315970 Sao Paulo - Brazil

^[2] Univ Sao Paulo, Fac Filosofia Ciencias & Letras, Dept Fis, Ave Bandeirantes 3900, BR-14040901 Ribeirao Preto - Brazil

^[3] Univ Aberdeen, Aberdeen 05508900 - Scotland

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 28, n. 3 MAR 2018.
• Citações Web of Science: 0

Resumo

The dynamics of a parametric simple pendulum submitted to an arbitrary angle of excitation phi was investigated experimentally by simulations and analytically. Analytical calculations for the loci of saddle-node bifurcations corresponding to the creation of resonant orbits were performed by applying Melnikov's method. However, this powerful perturbative method cannot be used to predict the existence of odd resonances for a vertical excitation within first order corrections. Yet, we showed that period-3 resonances indeed exist in such a configuration. Two degenerate attractors of different phases, associated with the same loci of saddle-node bifurcations in parameter space, are reported. For tilted excitation, the degeneracy is broken due to an extra torque, which was confirmed by the calculation of two distinct loci of saddle-node bifurcations for each attractor. This behavior persists up to phi approximate to 7 pi/180, and for inclinations larger than this, only one attractor is observed. Bifurcation diagrams were constructed experimentally for phi = pi/8 to demonstrate the existence of self-excited resonances (periods smaller than three) and hidden oscillations (for periods greater than three). Published by AIP Publishing. (AU)

• Processo FAPESP: 11/19296-1 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/07043-0 - Análise da turbulência e da propagação de estruturas em plasmas
• Beneficiário: Felipe Augusto Cardoso Pereira
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 17/04748-0 - Ferramentas de neuroinformática para modelagem declarativa multiescala via geração automática de implementações, com aplicações a modelagem de grande escala da retina de vertebrados
• Beneficiário: Bóris Marin
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado