Lie group generalized-α time integration of constrained flexible multibody systems

Brüls, Olivier; Cardona, Alberto; Arnold, Martin

doi:10.1016/j.mechmachtheory.2011.07.017

Cited by 136 publications

(119 citation statements)

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“…In a series of publications, the solution of the differential-algebraic equation (DAE) system (94) has been addressed with amended generalized α schemes that are known from computational structural mechanics. Brüls et al [32][33][34] introduced generalized α schemes adopting the concept of Lie group integration using canonical coordinates. In [34], the method was extended to MBS containing flexible bodies.…”

Section: Geometric Integration Of Mbs Models In Absolute Coordinatesmentioning

confidence: 99%

“…Brüls et al [32][33][34] introduced generalized α schemes adopting the concept of Lie group integration using canonical coordinates. In [34], the method was extended to MBS containing flexible bodies. It was observed that the direct and semidirect product representations lead to different numerical behavior.…”

Section: Geometric Integration Of Mbs Models In Absolute Coordinatesmentioning

confidence: 99%

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Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

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Section: Geometric Integration Of Mbs Models In Absolute Coordinatesmentioning

confidence: 99%

Section: Geometric Integration Of Mbs Models In Absolute Coordinatesmentioning

confidence: 99%

Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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“…Please refer to Uhlar and Betsch, 10 Bru¨ls et al, 11 Bru¨ls and Cardona, 12 Celledoni et al, 13 Celledoni and Owren, 14 and Mu¨ller and Terze 34 for some new developments on this topic.…”

Section: A Heavy Topmentioning

confidence: 99%

Dynamical equations of multibody systems on Lie groups

Pan

2015

Advances in Mechanical Engineering

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The Euler-Poinaré principle is a reduced Hamilton's principle under Lie group framework. In this article, it is applied to derive a hybrid set of dynamical equations of rigid multibody systems, which include four parts: the classical Euler-Lagrange equations of rigid bodies in their translational coordinates of mass center; Euler-Poinaré equations via orientation matrices and their related angular velocities; the constraint equations due to different joints in Cartesian coordinates and Lie groups; and the reconstruction equations between special orthogonal groups and their Lie algebras. The generalized mass matrices of dynamical equations are constant, which is computationally efficient. All the equations can be constructed systematically and can be solved easily. The construction equations can be used to design Lie group integrators of multibody system dynamics. The procedure presented in this article can be extended easily to flexible multibody systems, systems with non-holonomic constraints, and so on.

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“…Over the last decades, it has become apparent that many of the theoretical questions in this area of dynamics can be answered in an illustrative and complete way by employing fundamental concepts of differential geometry [4,17,18]. This in turn provides a stronger foundation in solving difficult engineering problems by employing new, more accurate and robust numerical techniques (e.g., [2,6,11]). Based on these observations, the main objective of this work is to use such concepts in order to treat a class of mechanical systems.…”

Section: Introductionmentioning

confidence: 99%