Articles | Volume 15, issue 1
https://doi.org/10.5194/ms-15-169-2024
https://doi.org/10.5194/ms-15-169-2024
Research article
 | 
12 Mar 2024
Research article |  | 12 Mar 2024

A Lie group variational integrator in a closed-loop vector space without a multiplier

Long Bai, Lili Xia, and Xinsheng Ge

Related subject area

Subject: Dynamics and Control | Techniques and Approaches: Mathematical Modeling and Analysis
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Cited articles

Abeywardena, S. and Chen, C.: Inverse dynamic modelling of a three-legged six-degree -of- freedom parallel mechanism, Multi. Sys. Dyn., 41, 1–24, https://doi.org/10.1007/s11044-016-9506-y, 2017. 
Algarin-Pinto, J. and Garza-Castanon, L.: Dynamic Modelling and Control of a Parallel Mechanism Used in the Propulsion System of a Biomimetic Underwater Vehicle, Appl. Sci.-Basel, 11, 4909, https://doi.org/10.3390/app11114909, 2021. 
Condurache, D.: Higher-Order Relative Kinematics of Rigid Body and Multibody Systems. A Novel Approach with Real and Dual Lie Algebras, Mech. Mach. Theo., 176, 104999, https://doi.org/10.1016/j.mechmachtheory.2022.104999, 2022. 
Condurache, D. and Popa, I.: A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions, Symmetry-Basel, 15, 2011, https://doi.org/10.3390/sym15112011, 2023. 
Condurache, D. and Sfartz, E.: Exact Closed-Form Solutions of the Motion in Non-Inertial Reference Frames Using the Properties of Lie Groups SO3 and SE3, Symmetry-Basel, 13, 1963, https://doi.org/10.3390/sym13101963, 2021. 
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The paper shows that the attitude vector expression for the rod can decrease the difficulty of derivation and expression of the dynamics model. Variation theory can package the closed-loop pose–attitude constraint in the dynamics model, so the constraint does not need to be considered explicitly. Using the geometry modelling method to build the dynamics model of a four-bar mechanism can avoid the repetitive operation of the closed-loop constraint.