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