多刚体动力学仿真的李群变分积分算法
作者:
作者单位:

1.北京理工大学 宇航学院力学系,北京 100081;2.北京空间飞行器总体设计部,北京 100094

作者简介:

E-mail: chenju0221@163.comE-mail:chenju0221@163.com

通讯作者:

中图分类号:

O313.7;O302

基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目)


LIE GROUP VARIATIONAL INTEGRATATION FOR MULTI-RIGID BODY SYSTEM DYNAMIC SIMULATION
Author:
Affiliation:

1.Department of Mechanics,School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;2.Beijing Institute of Spacecraft System Engineering,Beijing 100094,China

Fund Project:

The project supported by the National Natural Science Foundation of China(11832005)

  • 摘要
  • |
  • 图/表
  • |
  • 访问统计
  • |
  • 参考文献
  • |
  • 相似文献
  • |
  • 引证文献
  • |
  • 资源附件
  • |
  • 文章评论
    摘要:

    刚体的构形可用其质心位置和姿态矩阵描述.刚体的位置可以在欧几里得空间中表示,但是其姿态矩阵是在李群上演化的.由于李群独特的非线性性质,基于欧氏空间的多体动力学建模与数值算法难以完全真实地描述系统的动力学特性,特别是长时间历程的动力学特性.本文基于几何力学理论,首先根据离散Hamilton变分原理与离散Legendre变换,建立了多刚体系统的Hamilton体系李群变分积分公式.其次,给出李群变分积分公式的两种离散格式:一般离散格式和RATTLie离散格式.最后,采用这两种不同离散格式构建的算法计算了重力作用下空间刚体双摆的动力学问题,对比研究了算法在保持系统群结构、系统能量等方面的性质.计算结果表明,RATTLie离散格式较一般格式精度更高,且能更好地保持系统群结构与能量.

    Abstract:

    The configuration of rigid body can be described by its position vector and attitude matrix. The position vector can be accurately represented in a Euclidean space while the attitude matrix evolves on a Lie group. Due to the unique nonlinear properties of the Lie group, it’s difficult for the Euclidean space based modeling method and numerical algorithm to accurately capture the real dynamic characteristics of multibody systems, especially their long-time dynamic characteristics. Firstly, based on geometric mechanics theory, a Lie group variational integrator in the Hamilton system for simulating the multi-rigid body system dynamics is derived according to the discrete Hamilton’s principle and discrete Legendre transformation. Then, two different discrete forms of the Lie group variational integrator are further introduced, namely, the general Lie group variational integrator and the RATTLie variational integrator. Finally, the two established discrete algorithms are respectively used to study the dynamics of a spatial double pendulum under the gravity action, and their characteristics, such as the group structure preservation and system energy conservation, are comparatively studied. Numerical results indicate that compared to the general Lie group algorithm, the RATTLie algorithm can achieve a higher computational accuracy, better group structure preservation and energy conservation.

    参考文献
    相似文献
    引证文献
引用本文

黄子恒,陈菊,张志娟,田强.多刚体动力学仿真的李群变分积分算法[J].动力学与控制学报,2022,20(1):8~17; Huang Ziheng, Chen Ju, Zhang Zhijuan, Tian Qiang. LIE GROUP VARIATIONAL INTEGRATATION FOR MULTI-RIGID BODY SYSTEM DYNAMIC SIMULATION[J]. Journal of Dynamics and Control,2022,20(1):8-17.

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2021-01-19
  • 最后修改日期:2021-03-03
  • 录用日期:2021-03-09
  • 在线发布日期: 2022-03-04
  • 出版日期:

微信公众号二维码

手机版网站二维码