Periodic oscillations and attracting basins for a parametrically excited pendulum

Abstract

The parametrically excited pendulum exhibits a wide variety of non-linear behaviour. We consider numerical studies of periodic motion; the simple periodic solutions are also studied analytically using the harmonic balance method. For more complicated motions the problem is tackled by solving algebraic non-linear equations either using the definition of fixed points for Poincare map, or, where convenient, using a Galerkin technique; in both techniques the stability of solutions can also be checked. The cell mapping technique is used to study the attracting basins and to systematically assess the various types of periodic motions.