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math.DS2026
Koopman-based stability analysis of differential-algebraic equations with applications to frictional multibody systems
Alexander Schütz, Fabia Bayer, Remco I. Leine
Periodic solutions of differential-algebraic equations (DAEs) and ordinary differential equations (ODEs) can be determined using the harmonic balance method (HBM), which is a frequ…
math.DS2026
Model order reduction of piecewise linear mechanical systems using invariant cones
A. Yassine Karoui, Remco I. Leine
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for m…
math.DS2024★ 3 cited
Extended invariant cones as Nonlinear Normal Modes of inhomogeneous piecewise linear systems
A. Yassine Karoui, Remco I. Leine
The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invar…