this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating operator, reformulated as convex optimization problems linear...