Naslov
Modelling and Integration Concepts of Multibody Systems on Lie Groups

Autori
Muller, Andreas ; Terze, Zdravko

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Multibody Dynamics, Computational Methods and Applications

Urednik/ci
Terze, Zdravko

Izdavač
Springer

Grad
Cham : Heidelberg : New York : Dordrecht : London

Godina
2014

Raspon stranica
123-143

ISBN
978-3-319-07260-9

Ključne riječi
Lie group integration, Rigid body dynamics, Multibody systems, Constraint satisfaction, Screw systems, Munthe-Kaas scheme, Motion integrals, Coadjoint orbits preservation, Angular momentum conservation

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Strojarstvo, Zrakoplovstvo, raketna i svemirska tehnika

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