41 Reduced Order Models for Systems with Disparate Spatial and Temporal Scales 453 0.2 0.25 0.3 0.35 −0.1 −0.05 0 0.05 0.1 x30 x30 q0 =0.05 0.2 0.25 0.3 0.35 −0.1 −0.05 0 0.05 0.1 x30 x30 q0 =0.05 −0.5 0 0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 x30 ˙x30 q0 =0.12 −0.5 0 0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 x30 ˙x30 q0 =0.12 −0.5 0 0.5 −0.4 −0.2 0 0.2 0.4 x30 ˙x30 q0 =0.22 −0.5 0 0.5 −0.4 −0.2 0 0.2 0.4 x30 ˙x30 q0 =0.22 −1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 x30 ˙x30 q0 =0.35 −1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 x30 ˙x30 q0 =0.35 Fig. 41.4 Phase portraits of the 30th mass of the nonlinear system obtained from full scale (blue) and reduced order models (red): four-dimensional SOD-based ROMs (left); four-dimensional separated SOD-based ROMs (right)
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