Modelling and Integration Concepts of Multibody Systems on Lie Groups

Müller, Andreas and Terze, Zdravko (2014) Modelling and Integration Concepts of Multibody Systems on Lie Groups. = Modelling and Integration Concepts of Multibody Systems on Lie Groups. In: Multibody Dynamics, Computational Methods and Applications. Computational Methods in Applied Sciences, Vol. 35 . Springer, Cham, Heidelberg, New York, Dordrecht, London, pp. 123-143. ISBN 978-3-319-07260-9

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Lie group integration schemes for multibody systems (MBS) are attractive as they provide a coordinate-free and thus singularity-free approach to MBS modeling. The Lie group setting also allows for developing integration schemes that preserve motion integrals and coadjoint orbits. Most of the recently proposed Lie group integration schemes are based on variants of generalized alpha Newmark schemes. In this chapter constrained MBS are modeled by a system of differential-algebraic equations (DAE) on a configuration being a subvariety of the Lie group SE(3)^n. This is transformed to an index 1 DAE system that is integrated with Munthe-Kaas (MK) integration scheme. The chapter further addresses geometric integration schemes that preserve integrals of motion. In this context, a non-canonical Lie-group Störmer-Verlet integration scheme with direct SO(3) rotational update is presented. The method is 2nd order accurate, it is angular momentum preserving, and it does not introduce a drift in the energy balance of the system. Moreover, although being fully explicit, the method achieves excellent conservation of the angular momentum of a free rotational body and the motion integrals of the Lagrangian top. A higher-order coadjoint-preserving integration on SO(3) scheme is also presented. This method exactly preserves spatial angular momentum of a free body and it is particularly numerically efficient.

Item Type: Book Section
Keywords (Croatian): Lie group integration, Rigid body dynamics, Multibody systems, Constraint satisfaction, Screw systems, Munthe-Kaas scheme, Motion integrals, Coadjoint orbits preservation, Angular momentum conservation
Subjects: NATURAL SCIENCES > Mathematics
TECHNICAL SCIENCE > Mechanical Engineering
TECHNICAL SCIENCE > Aviation, rocket and space technology
Divisions: 1300 Department of Aeronautical Engineering > 1320 Chair of Aircraft Dynamics
Date Deposited: 22 Sep 2016 13:24
Last Modified: 22 Sep 2016 13:24

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