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Research Papers

On the Use of Lie Group Time Integrators in Multibody Dynamics

[+] Author and Article Information
Olivier Brüls1

Department of Aerospace and Mechanical Engineering (LTAS), University of Liège, Chemin des Chevreuils 1, B52/3, 4000 Liège, Belgiumo.bruls@ulg.ac.be

Alberto Cardona

CIMEC-INTEC, Universidad Nacional Litoral-Conicet, Güemes 3450, 3000 Santa Fe, Argentinaacardona@intec.unl.edu.ar

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(3), 031002 (May 14, 2010) (13 pages) doi:10.1115/1.4001370 History: Received March 25, 2009; Revised October 02, 2009; Published May 14, 2010; Online May 14, 2010

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parametrization problem. As an extension of the classical generalized-α method for dynamic systems, it can deal with constrained equations of motion. Second-order accuracy is demonstrated in the unconstrained case. The performance is illustrated on several critical benchmarks of rigid body systems with high rotation speeds, and second-order accuracy is evidenced in all of them, even for constrained cases. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control, and optimization of multibody systems.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 2

Rotating body with spherical ellipsoid of inertia and follower torque. Error norm evaluated at t=0.42:0.02:0.6 s.

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Figure 3

Free rotating body. Error norm evaluated at t=0.82:0.02:1 s

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Figure 4

Free rotating body. Trajectories in x-y plane for all algorithms, compared with analytical solution

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Figure 5

Rotating body with follower torque. Error norm evaluated at t=0.12:0.02:0.3 s.

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Figure 6

Heavy top (without kinematic constraints). Error norm evaluated at t=0.32:0.02:0.5 s.

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Figure 7

Heavy top (with kinematic constraints)

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Figure 8

Heavy top (with kinematic constraints)

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