Model reduction for constrained mechanical systems via spectral submanifolds

Abstract Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular, multibody commonly configuration that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation such constrained problems is challenging, making reduced-order models (ROMs) paramount importance. this work, we show how use spectral submanifolds (SSMs) construct rigorous ROMs for mechanical constraints. These SSM-based enable direct extraction backbone curves and forced response facilitate efficient bifurcation analysis. We demonstrate effectiveness reduction procedure on several examples varying complexity, including nonlinear finite-element systems. also provide an open-source implementation proposed method contains all details our examples.