The period of a whirling pendulum
The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point.
Limit cycles in the equation of whirling pendulum with autonomous perturbation
The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.
Saddle connections in planar systems
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