Articles | Volume 15, issue 1
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,, 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,, 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,, 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,, 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,, 2021. 
Short summary
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.