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Non rotating periodic orbits in the parametrically excited pendulum. (English) Zbl 0809.70015

Summary: Non-rotating solutions for the parametrically excited pendulum are considered, and comparison is made between the pendulum and a system which permits escape from a symmetric potential well. Two escape or failure scenarios are identified by a bifurcation diagram, and stable periodic orbits are identified using methods of symbolic dynamics and path following techniques.

MSC:

70K28 Parametric resonances for nonlinear problems in mechanics
37G99 Local and nonlocal bifurcation theory for dynamical systems
37E99 Low-dimensional dynamical systems
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