| 多体系统动力学Lie 群微分⁃代数方程约束稳定方法 |
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| 引用本文： | 李亚男,李博文,丁洁玉,潘振宽. 多体系统动力学Lie 群微分⁃代数方程约束稳定方法[J]. 动力学与控制学报, 2018, 16(2): 97-101. DOI: 10.6052/1672?6553?2018?006 |
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| 作者姓名： | 李亚男 李博文 丁洁玉 潘振宽 |
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| 作者单位： | 1. 青岛大学数学与统计学院,青岛,266071;2. 青岛大学数学与统计学院,青岛 266071;3. 青岛大学计算力学与工程仿真研究中心,青岛 266071;4. 青岛大学计算机科学技术学院,青岛,266071 |
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| 基金项目： | 国家自然科学基金项目(11472143 |
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| 摘 要： | 针对多体系统动力学微分-代数方程求解问题,研究基于Lie群表达的约束稳定方法.首先引入新的Lagrange乘子,结合位移约束、速度级约束和加速度级约束方程,构造了新的Lie群微分-代数方程.然后使用向后差商隐式方法和CG(Crouch-Grossman)方法,对微分–代数方程进行离散求解,得到精确度较高的动力学仿真结果.该方法在精确保持各级约束方程的同时,保持旋转矩阵的正交性,并且使系统总能量误差较小.
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| 关 键 词： | 多体系统动力学 微分?代数方程 Lie群 约束稳定 multibody system dynamics different?algebraic equations(DAEs) Lie group constraint sta?bilization |
| 收稿时间： | 2017-09-20 |
| 修稿时间： | 2017-11-21 |
Constraints stabilization method for daes on lie group of multibody system dynamics |
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| Li Yanan,Li Bowen,Ding Jieyu and Pan Zhenkuan. Constraints stabilization method for daes on lie group of multibody system dynamics[J]. Journal of Dynamics and Control, 2018, 16(2): 97-101. DOI: 10.6052/1672?6553?2018?006 |
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| Authors: | Li Yanan Li Bowen Ding Jieyu Pan Zhenkuan |
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| Affiliation: | 1.School of Mathematics and Statistics, Qingdao266071;2.Center for Computational Mechanics and Engineering Simulation, Qingdao266071;3.College of Computer Science and Technology, Qingdao266071; |
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| Abstract: | Constraints stabilization method on Lie group is studied for different-algebraic equations (DAEs) of multibody system dynamics. Considering the displacement constraints, the velocity constraints and the acceleration constraints equations, the new Lagrange multipliers are used to construct the new DAEs on Lie groups. Then, using the ward difference method and CG (Crouch-Grossman) method, high accuracy simulation results is obtained by solving the constraints stabilization DAEs. The constraints stabilization method can accurately maintain the constraint equation at all levels, and can maintain the orthogonality of rotation matrix. Meanwhile, the total energy error of the system is smaller. © 2018 Journal of Dynamics and Control. All rights reserved. |
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| Keywords: | Constraint stabilization Different-algebraic equations(DAEs) Lie group Multibody system dynamics |
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