Summary
The dynamics of the primary Spectral Submanifold (SSM) constructed over the eigenspace spanned by the slowest modes of a dynamical system represent an ideal reduced order model. However, modeling the dynamics of trajectories lying farther away from the primary SSM is difficult if the system exhibits non-normal behavior. In the present work, we address how to apply the primary SSM-based model reduction technique to systems featuring non-orthogonal slow and fast eigenspaces in both linear and nonlinear problems. In particular, the reduced coordinates parametrizing the SSM are found via an oblique projection of the coordinates of the observed space. The projection is constructed minimizing the oscillations of the instantaneous relationship between frequency and amplitude (backbone curves) of decaying trajectories.
