Study on Symmetries and Conserved Quantities of Mechanical Multibody System Collision Dynamics

ZHENG Mingliang; FENG Xian; LI Wenxia; CAO Yalin

doi:10.21656/1000-0887.380291

Volume 39 Issue 11

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ZHENG Mingliang, FENG Xian, LI Wenxia, CAO Yalin. Study on Symmetries and Conserved Quantities of Mechanical Multibody System Collision Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1292-1299. doi: 10.21656/1000-0887.380291

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Study on Symmetries and Conserved Quantities of Mechanical Multibody System Collision Dynamics

doi: 10.21656/1000-0887.380291

Wuxi Taihu University, Wuxi, Jiangsu 214064, P.R.China

Received Date: 2017-11-21
Rev Recd Date: 2018-03-17
Publish Date: 2018-11-01

Abstract

Abstract

To provide a powerful new tool for quantitative and qualitative analysis of collision dynamics in complex mechanical multibody systems, the symmetry theory in modern analytical mechanics was introduced into the study of mechanical multibody external collision dynamics. Firstly, the Euler-Lagrange equation of collision dynamics was derived based on the momentum method; secondly, the group theory was introduced, then, according to the invariance principle, the condition equations for the Noether symmetry and the Lie symmetry were obtained and the corresponding conserved quantity form was got, which made possible an effective approach to the analytic integral theory for dynamic equations. Finally, the collision dynamics of a planar open-loop 2-connecting-rod mechanism was taken as an example for application and analysis. Research shows that deeper mechanical laws and motion characteristics of mechanical multibody system collision dynamics can be obtained by means of symmetries and conserved quantities, and the results also lay a theoretical foundation for more precise dynamic optimal design and advanced control.
- mechanical multibody system,
- Euler-Lagrange equation,
- symmetry,
- conserved quantity,
- plane connecting rod

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References

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