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Bifurcation Trees of Periodic Motions in a Parametrically Excited Pendulum

[+] Author Affiliations
Yu Guo

Midwestern State University, Wichita Falls, TX

Albert C. J. Luo

Southern Illinois University, Edwardsville, IL

Paper No. DETC2017-67161, pp. V006T10A060; 8 pages
doi:10.1115/DETC2017-67161
From:
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5820-2
  • Copyright © 2017 by ASME

abstract

In this paper, the bifurcation trees of periodic motions in a parametrically excited pendulum are studied using discrete implicit maps. From the discrete maps, mapping structures are developed for periodic motions in such a parametric pendulum. Analytical bifurcation trees of periodic motions to chaos are developed through the nonlinear algebraic equations of such implicit maps in the specific mapping structures. The corresponding stability and bifurcation analysis of periodic motions is carried out. Finally, numerical results of periodic motions are presented. Many new periodic motions in the parametrically excited pendulum are discovered.

Copyright © 2017 by ASME

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