Computational Flexible Multibody Dynamics

Simeon, Bernd

doi:10.1007/978-3-642-35158-7

Cited by 60 publications

(56 citation statements)

References 93 publications

(145 reference statements)

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“…To summarize, PDEs with constraints such as the Navier-Stokes equations often feature a rich structure that should be exploited, and building on the available PDE methodology reveals interesting cross-connections with the differential-algebraic viewpoint. In this context, the abstract formulation (50) as transient saddle point problem defines a rather broad problem class where many application fields can be subsumed [Sim13].…”

Section: Examples For Pdaesmentioning

confidence: 99%

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On the History of Differential-Algebraic Equations

Simeon

2017

Surveys in Differential-Algebraic Equations IV

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Section: Examples For Pdaesmentioning

confidence: 99%

“…More precisely, by introducing suitable operators, the pantograph and catenary model can be written as [Sim13] u + Au + B ′ λ = l, (55a) Bu = m,…”

Section: Pantograph and Catenarymentioning

confidence: 99%

On the History of Differential-Algebraic Equations

Simeon

2017

Surveys in Differential-Algebraic Equations IV

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“…The computational efficiency and stability of these dynamical equations depend strongly on the configuration description of multibody systems [1][2][3][4][5][6][7][8][9] and especially on the expressions of the orientations of bodies.…”

Section: Introductionmentioning

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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“…The Lagrangian system (1a)-(1d) boils down to a differential-algebraic equation (DAE) of index 3 [24,56],…”

Section: Bilaterally Constrained Systemsmentioning

confidence: 99%