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.
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