Bifurcations of phase portraits of pendulum with vibrating suspension point

Neishtadt, Anatoly; Sheng, K.

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Bifurcations of phase portraits of pendulum with vibrating suspension point

journal contribution

posted on 2016-12-14, 14:56 authored by Anatoly NeishtadtAnatoly Neishtadt, K. Sheng

We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give a complete description of bifurcations of phase portraits of this averaged system.

History

School

Science

Department

Mathematical Sciences

Published in

Communications in Nonlinear Science and Numerical Simulation

Volume

47

Pages

71–80

Citation

NEISHTADT, A. and SHENG, K., 2016. Bifurcations of phase portraits of pendulum with vibrating suspension point. Communications in Nonlinear Science and Numerical Simulation, 47, pp. 71–80.

Publisher

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2016-11-03

Publication date

2016-11-12

Copyright date

2017

Notes

This paper was accepted for publication in the journal Communications in Nonlinear Science and Numerical Simulation and the definitive published version is available at http://dx.doi.org/10.1016/j.cnsns.2016.11.003.