基于高斯原理的多体系统动力学建模

刘延柱

doi:10.6052/0459-1879-14-143

基于高斯原理的多体系统动力学建模

doi: 10.6052/0459-1879-14-143

刘延柱

上海交通大学工程力学系, 上海 200240

基金项目: 国家自然科学基金资助项目(11392195).

详细信息

作者简介:
刘延柱,教授,主要研究方向:动力学与控制.

中图分类号: O316;O313;V423
计量
- 文章访问数: 1402
- HTML全文浏览量: 71
- PDF下载量: 1435
- 被引次数: 0
出版历程
- 收稿日期: 2014-05-21
- 修回日期: 2014-07-11
- 刊出日期: 2014-11-18

DYNAMIC MODELING OF MULTI-BODY SYSTEM BASED ON GAUSS'S PRINCIPLE

Liu Yanzhu

Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China

Funds: The project was supported by the National Natural Science Foundation of China (11392195).

摘要

摘要: 基于高斯最小拘束原理,以释放中的绳系卫星为背景,建立地球引力场内变长度大变形柔索联系的多体系统动力学模型. 利用基尔霍夫动力学比拟方法将柔索的变形转化为刚性截面沿中心线的转动,使包含刚性分体与变形体的刚柔耦合系统转化为由柔索的刚性截面与刚性分体组成的广义多刚体系统. 由于刚性截面的局部小变形沿弧坐标的积累不受限制,适合描述柔索的超大变形. 文中对此刚柔耦合多体系统导出其在地球引力场中的拘束函数,考虑各分体在空间中相对位置的几何约束条件,利用拉格朗日乘子构成以条件极值问题为特征的数学模型. 将高斯原理用于多体系统动力学的建模,其特点是以寻求函数极值的变分方法代替微分方程,通过数值计算直接得出运动规律. 其形式统一,不随系统拓扑结构的变化而改变,也无需区分树系统或非树系统.对于带控制的多体系统,动力学分析还可根据技术需要与系统的优化结合进行.
- 高斯最小拘束原理 /
- 多体系统动力学 /
- 基尔霍夫弹性杆模型 /
- 绳系卫星
Abstract: Based on the Gauss's principle of least constraint, the dynamic modeling of a multi-body system connected by an elastic cable with varied lengths and large deformation in gravitational field of the earth was proposed in this paper. The practical background of the topic is the release process of a tethered satellite. The Kirchhoff's method was applied to transform the deformation of the elastic cable to rotation of rigid cross section along the centerline of the cable. Since the local small deformation of the cable can be accumulated limitlessly along the arc-coordinate, the Kirchhoff's model is suitable to describe the super-large deformation of elastic rod. In present paper the Gauss's constraint function of the system of rigid-flexible bodies in gravitational field of the earth was derived, and the geometric constraint conditions concerning relative position of bodies in space were considered using the Lagrange's multipliers. Therefore the dynamical model of the system was established in the form of conditional extremum problem. Applying the approach of Gauss's principle the real motion of the system can be obtained by the variation method directly through seeking the minimal value of constraint function without differential equations. The unified form of the model does not changed for different topologic constructions of the system, and it is unnecessary to distinct the tree system or system with loops. In the case of multi-body system with automatic control, the dynamic analysis can be combined with the optimization for different technique objectives.
- Gauss's principle of least constraint /
- dynamics of multi-body systems /
- Kirchhoff's model of elastic rod /
- tethered satellite

HTML全文

参考文献(15)

刘延柱. 高等动力学. 北京: 高等教育出版社,2001 (Liu Yanzhu. Advanced Dynamics. Beijing: High Education Press, 2001(in Chinese))

Popov EP, Vereshchagin AF, Zenikevich S. Manipulation Robot, Dynamics and Algorithm. Moscow. Science, 1978 (in Russian)

Lilov L, Lorer M. Dynamic analysis of multi-rigid-body systems based on the Gauss principle. ZAMM, 1982, 62(10): 539-545

Kalaba1 RE, Udwadia1 FE. Equations of motion for nonholonomic, constrained dynamical systems via Gauss's principle. Transactions of the ASME, 1993, 60: 662-668

Bruyninckx H, Khatib O. Gauss' principle and the dynamics of redundant and constrained manipulators. In: Proceedings of the 2000 IEEE International Conference on Robotics & Automation, 2000: 2563-2569

Kalaba R, Natsuyama H, Udwadia F. An extension of Gauss's principle of least constraint. Int J General Systems, 2004, 33(1): 63-69

刘延柱,潘振宽,戈新生. 多体系统动力学(第二版).北京:高等教育出版社,2014 (Liu Yanzhu, Pan Zhenkuan, Ge Xinsheng. Dynamics of Multibody Systems. Beijing: High Education Press, 2014 (in Chinese))

董龙雷,阎桂荣,杜彦亭等. 高斯最小拘束原理在一类刚柔耦合系统分析中的应用. 兵工学报,2001, 22(3): 347-351 (Dong Longlei, Yan Guirong, Du Yanting, et al. Application of Gauss minimum constraint principle in a rigid-flexible coupled system. Acta Armamantanii, 2001, 22(3): 347-351 (in Chinese))

史跃东, 王德石. 舰炮振动的高斯最小拘束分析方法. 海军工程大学学报,2009,21(5): 1-5 (Shi Yuedong, Wang Deshi. Application of Gauss minimum constraint principle in gun vibration analysis. J Naval Univ of Engng, 2009,21(5): 1-5 (in Chinese))

郝名望,叶正寅. 单柔体与多柔体动力学的高斯最小拘束原理. 广西大学学报,2011, 36(2): 195-204 (Hao Mingwang, Ye Zhengyin. Gauss principle of least constraint of simple flexible body and multi-flexible body dynamics. J Guangxi Univ, Nat Sci Ed, 2011, 36(2): 195-204 (in Chinese))

薛纭,翁德玮. 超细长弹性杆动力学的Gauss原理,物理学报,2009,58(1):34-39 (Xue Yue, Weng Dewei. Gauss principle for a super-thin elastic rod dynamics. Acta Phys. Sin, 2009, 58(1): 34-39 (in Chinese))

Wen H, Jin DP, Hu HY. Advances in dynamics and control of tethered satellite systems. Acta Mechanica Sinica, 2008, 24(3): 229-241

余本嵩,文浩,金栋平. 时变自由度绳系卫星系统动力学. 力学学报,2010, 42(5): 926-932 (Yu BS, Wen H, Jin DP. Dynamics of tethered satellite system with a time-varying number of degrees-of-freedom. Acta Mechanica Sinica, 2010, 42(5): 926-932 (in Chinese))

Liu Y, Sheng L. Stability and vibration of a helical rod constrained by a cylinder. Acta Mechanica Sinica, 2007, 23: 215-219

刘延柱. 大变形轴向运动梁的精确动力学模型. 力学学报,2012, 44(5): 832-838 (Liu Yanzhu. Exact dynamical model of axially moving beam with large deformation. Acta Mechanica Sinica, 2012, 44(5): 832-838 (in Chinese))

施引文献

资源附件(0)

访问统计