Limit cycles in the equation of whirling pendulum with autonomous perturbation.
The paper deals with a two-parameter Hamiltonian system with an autonomous perturbation which models a whirling pendulum. Using the Melnikov function method, the author proves the existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters. After a short description of local bifurcations of the system, the global analysis of the phase portrait is given by means of the study of properties of the Melnikov function whose zeros correspond to limit cycles. The needed properties of the Melnikov function the author gets either by a direct study of corresponding elliptic integrals and by the Li and Zhang criterion, which allows one to examine the monotonicity of the ratio of two Abelian integrals without calculating them.
scientific article; zbMATH DE number 2165523