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Structure-preserving integrators based on a new variational principle for constrained mechanical systems

Kinon, Philipp L. ORCID iD icon 1; Betsch, Peter 1; Schneider, Simeon 1
1 Institut für Mechanik (IFM), Karlsruher Institut für Technologie (KIT)

Abstract:

A new variational principle for mechanical systems subject to holonomic constraints is presented. The newly proposed GGL principle is closely related to the often used Gear-Gupta-Leimkuhler (GGL) stabilization of the differential–algebraic equations governing the motion of constrained mechanical systems. The GGL variational principle relies on an extension of the Livens principle (sometimes also referred to as Hamilton–Pontryagin principle) to mechanical systems subject to holonomic constraints. In contrast to the original GGL stabilization, the new approach facilitates the design of structure-preserving integrators. In particular, new variational integrators are presented, which result from the direct discretization of the GGL variational principle. These variational integrators are symplectic and conserve momentum maps in the case of systems with symmetry. In addition to that, a new energy–momentum scheme is developed, which results from the discretization of the Euler–Lagrange equations pertaining to the GGL variational principle. The numerical properties of the newly devised schemes are investigated in representative examples of constrained mechanical systems.


Verlagsausgabe §
DOI: 10.5445/IR/1000160018
Veröffentlicht am 04.07.2023
Originalveröffentlichung
DOI: 10.1007/s11071-023-08522-7
Scopus
Zitationen: 3
Web of Science
Zitationen: 2
Dimensions
Zitationen: 6
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mechanik (IFM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2023
Sprache Englisch
Identifikator ISSN: 0924-090X, 1573-269X
KITopen-ID: 1000160018
Erschienen in Nonlinear Dynamics
Verlag Springer
Band 111
Heft 15
Seiten 14231–14261
Vorab online veröffentlicht am 14.06.2023
Schlagwörter Livens principle, Holonomic constraints, GGL principle, GGL stabilization, Index reduction, Structure-preserving integration, Variational integrators, Energy–momentum methods
Nachgewiesen in Dimensions
Web of Science
Scopus
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