Model reduction for constrained mechanical systems via spectral submanifolds

Mingwu Li*, Shobhit Jain, George Haller

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
59 Downloads (Pure)


Dynamical systems are often subject to algebraic constraints in conjunction with 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 multibody systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.

Original languageEnglish
Pages (from-to)8881-8911
Number of pages31
JournalNonlinear Dynamics
Issue number10
Publication statusPublished - 2023


  • Configuration constraints
  • Forced response curves
  • Invariant manifolds
  • Reduced-order models
  • Spectral submanifolds


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  • SSMTool

    Jain, S. (Creator), Thurnher, T. (Contributor), Li, M. (Contributor) & Haller, G. (Contributor), GitHub/Zenodo, 18 Oct 2022

    Dataset/Software: Software

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