Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters

Holzinger, Stefan; Gerstmayr, Johannes

doi:10.1115/1.0001759v

Cited by 1 publication

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the first investigations, we consider the heavy top without kinematic constraints according to Refs. [1,3,10,11,28]. In Fig.…”

Section: Heavy Top Without Kinematic Constraintsmentioning

confidence: 98%

“…The composition operation Eq. (A10) enables a singularity-free update of the rotation vector and can be evaluated without restrictions [10,11].…”

Section: Appendix a Implementation Details A1 Tangent Operatorsmentioning

confidence: 99%

“…[7,8]. They not only enable a singularity-free representation of spatial rotations [9], they also allow the use of three rotation parameters to model MBS [10,11] and even make the unit length constraint equation obsolete when integrating Euler parameters [3,12]. Moreover, LGIM allow the modelling of MBS with local velocity coordinates [13] and the so-called "local frame approach" [14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Holzinger

Arnold

Gerstmayr

2023

Preprint

Self Cite

View full text Add to dashboard Cite

As commonly known, standard time integration of the kinematic equations of rigid bodies modelled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using several typical rigid multibody systems. It is shown, that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turned out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the average number of Newton iterations required per time step is most often smaller for the Lie group integration method. It also turns out, that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.

show abstract

“…In the first investigations, we consider the heavy top without kinematic constraints according to Refs. [1,3,10,11,28]. In Fig.…”

Section: Heavy Top Without Kinematic Constraintsmentioning

confidence: 98%

“…The composition operation Eq. (A10) enables a singularity-free update of the rotation vector and can be evaluated without restrictions [10,11].…”

Section: Appendix a Implementation Details A1 Tangent Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Holzinger

Arnold

Gerstmayr

2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters

Cited by 1 publication

References 0 publications

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Contact Info

Product

Resources

About