Bifurcations of Oscillatory and Rotational Solutions of Double Pendulum with Parametric Vertical Excitation

Figure 3

Bifurcation diagrams of oscillations of the double pendulum (Figure 1) in two-parameter space (𝛾,𝛽) using 2 methods. (a) Curves from Figure 2(a) (1 : 1 : 1 resonance). (b) Detailed view in Figure 3(b). (c) Curves from Figure 2(c) (2 : 1 : 1 resonance). Initial conditions for numerical integration (𝜃₁=𝜋, 𝜃̇₁=−5, 𝜃₂=𝜋−0.01, and 𝜃̇₂=5). Abbreviations of bifurcations: SN: saddle-node, PD: period doubling, and SB: symmetry breaking.

(a)

(b)

(c)