Abstract
The 2:2 mode interaction of a parametrically excited double pendulum is explored in the excitation frequency/excitation amplitude plane. To determine the bifurcation structure at small amplitudes of oscillation, the method of averaging combined with centre manifold reduction is used. The full equations are solved numerically to extend the bifurcation set to larger amplitudes of response. Numerical centre manifold reduction is employed to derive two maps, valid near two multiple bifurcation points which organise the dynamical phenomena of the mode interaction region. Iteration of these maps shows the existence of global bifurcations. These results are discussed in the light of numerical integrations which show that a whole range of interesting behaviour occurs including torus doubling, torus ‘gluing’ and chaos.
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