Multibody System Dynamics

, Volume 30, Issue 2, pp 185–197 | Cite as

A new switching strategy for addressing Euler parameters in dynamic modeling and simulation of rigid multibody systems



This paper presents a new numerical strategy to address the extraneous coordinates in the Euler parameters. These parameters are unit quaternions with four variables, which have been used to describe the three rotational degrees-of-freedom (DOF) of a rigid body. This redundancy avoids the singularity issue that appears in the other rotational description methods including, Euler angles (3 parameters), direction cosines (9 parameters), and the Rodrigues parameters (3 parameters). However, these parameters must satisfy a normality constraint. A numerical and online constraint embedding method is invoked to address this holonomic constraint implicitly. It leads to a reduction of the equations of motion to a minimal form. However, the proposed method requires a procedure for the selection of the dependent Euler parameters. Several alternatives were examined and the best one is proposed as the method to use in this situation. They check specific conditions including, condition number of the mass and constraint matrices, to make a decision about retaining or switching the current dependent parameter. The effectiveness of the three different selection algorithms are examined using a 3D double pendulum with ball-and-socket joints. The results show the ability of the proposed strategy to handle drifting and singularity issues.


Rigid multibody dynamics Euler parameters Holonomic constraint Constraint embedding 


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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringThe University of Texas at ArlingtonArlingtonUSA

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