Comparison of long time simulation of Hamilton and Lagrange geometry dynamical models of a multibody system

• Autorzy: Bai Long , Ge Xinsheng , Xia Lili

Identyfikatory

DOI

10.15632/jtam-pl/156163

• Języki publikacji: EN

Abstrakty

EN

The geometry dynamical modeling method for a double pendulum is explored with the Lie group and a double spherical space method. Four types of Lagrange equations are built for relative and absolute motion with the above two geometry methods, which are then used to explore the influence of different expressions for motion on the dynamic modeling and computations. With Legendre transformation, the Lagrange equations are transformed to Hamilton ones which are dynamical models greatly reduced. The models are solved by the same numerical method. The simulation results show that they are better for the relative group than for the absolute one in long time simulation with the same numerical computations. The Lie group based result is better than the double spherical space one.

Słowa kluczowe

EN

double pendulum; Lie group; double spherical space; Lagrange; Hamilton equations

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2022
• Tom: Vol. 60 nr 4
• Strony: 687--704
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Bai Long

• Beijing Information Science and Technology University, Mechanical Electrical Engineering School, China
• Beijing Information Science and Technology University, School of Applied Science, China

autor

Ge Xinsheng

• Beijing Information Science and Technology University, Mechanical Electrical Engineering School, China
• Beijing Information Science and Technology University, School of Applied Science, China

autor

Xia Lili

• Beijing Information Science and Technology University, Mechanical Electrical Engineering School, China
• Beijing Information Science and Technology University, School of Applied Science, China

Bibliografia

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• 5. Ding J.Y., Pan Z.K., Zhang W., 2019, The constraint- stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics, Advances in Mechanical Engineering, 11, 4.
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• 8. Müller A., 2014, Higher derivatives of the kinematic mapping and some applications, Mechanism and Machine Theory, 76, 70-85.
• 9. Müller A., 2021, Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems, Proceedings of the Royal Society of London. Series A, 477, 20210303.
• 10. Müller A., 2022, Dynamics of parallel manipulators with hybrid complex limbs-Modular modeling and parallel computing, Mechanism and Machine Theory, 167, 104549.
• 11. Müller A., Terze Z., 2014, The significance of the configuration space Lie group for the constraint satisfaction in numerical time integration of multibody systems, Mechanism and Machine Theory, 82, 173-202.
• 12. Rong J., Wu Z., Liua C., Brüls O., 2020, Geometrically exact thin-walled beam including warping formulated on the special Euclidean group SE(3), Computer Methods in Applied Mechanics and Engineering, 369, 113062.
• 13. Sonneville V., Brüls O., 2014, Sensitivity analysis for multibody systems formulated on a Lie group, Multibody System Dynamcis, 31, 1, 47-67.
• 14. Terze Z., Müller A., Zlatar D., 2015, Lie-group integration method for constrained multibody systems in state space, Multibody System Dynamics, 34, 275-305.
• 15. Urkullu G., de Bustos I.F., García-Marina V., Uriarte H., 2019, Direct integration of the equations of multibody dynamics using central differences and linearization, Mechanism and Machine Theory, 133, 432-458.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).