Inertia plays a crucial role in the quaternion-based rigid body dynamics, the associated mass matrix, however, presents singularity in the traditional representation. Recent researches demonstrated that the singularity can be avoided by adding an extra term into kinetic energy via a multiplier. Here, we propose a modified inertia representation through splitting the kinetic energy into two parts, where a square term of quaternion velocity, governed by an extra inertial parameter, is separated from the original expression. We further derive new numerical integration schemes in both Lagrange and Hamilton framework. Error estimation shows that the extra inertial parameter has a significant influence on the numerical error in discretization, and an iterative scheme of optimizing the extra inertial parameter to reduce the numerical error in simulation is proposed for quaternion-based rigid body dynamics. Numerical results demonstrate that the mean value of the three principal moments of inertia is a reasonable value of the extra inertia parameter which can impressively improve the accuracy in most cases, and the iterative scheme can further reduce the numerical error for numerical integration, taking the implementation in Lagrange's frame as an example.
On the Numerical Influences of Inertia Representation for Rigid Body Dynamics in Terms of Unit Quaternion
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 7, 2015; final manuscript received March 12, 2016; published online March 29, 2016. Assoc. Editor: Alexander F. Vakakis.
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Xu, X., and Zhong, W. (March 29, 2016). "On the Numerical Influences of Inertia Representation for Rigid Body Dynamics in Terms of Unit Quaternion." ASME. J. Appl. Mech. June 2016; 83(6): 061006. https://doi.org/10.1115/1.4033031
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