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.
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.
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.