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Limit cycles in the equation of whirling pendulum with autonomous perturbation

Hana Lichardová — 1999

Applications of Mathematics

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

Hana Lichardová — 2000

Archivum Mathematicum

The period of a whirling pendulum

Hana Lichardová — 2001

Mathematica Bohemica

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.

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