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


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.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 5

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

Grahic Jump Location
Figure 6

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

Grahic Jump Location
Figure 7

Heavy top (with kinematic constraints)

Grahic Jump Location
Figure 8

Heavy top (with kinematic constraints)

Grahic Jump Location
Figure 4

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

Grahic Jump Location
Figure 3

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

Grahic Jump Location
Figure 2

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In