力学与实践 ›› 2015, Vol. 37 ›› Issue (4): 488-491,487.DOI: 10.6052/1000-0879-15-096

• 应用研究 • 上一篇    下一篇

优化形式的刚体系统动力学模拟

杨流松1, 姚文莉1, 岳嵘2   

  1. 1. 青岛理工大学理学院, 山东青岛 266520;
    2. 山东科技大学数学学院, 山东青岛 266590
  • 收稿日期:2015-04-09 修回日期:2015-05-01 出版日期:2015-08-15 发布日期:2015-08-25
  • 通讯作者: 姚文莉,E-mail:ywenli1969@sina.com
  • 基金资助:

    国家自然科学基金资助项目(10872118, 11272167).

SIMULATION OF BODY DYNAMICS WITH OPTIMIZATION

YANG Liusong1, YAO Wenli1, YUE Rong2   

  1. 1. College of Science, Qingdao Technological University, Qingdao 266520, Shandong, China;
    2. College of Mathematics, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
  • Received:2015-04-09 Revised:2015-05-01 Online:2015-08-15 Published:2015-08-25

摘要:

基于广义坐标形式的高斯最小拘束原理来研究刚体系统的动力学问题的优化方法. 相比目前动力学建模普遍采用的质点形式的高斯最小拘束原理,广义坐标形式的高斯最小拘束原理因对所选择的广义坐标没有要求,而使得建模过程更简单及具有更强的通用性. 本文分别建立了有约束和无约束条件下问题的优化动力学模型,对问题进行了动力学数值模拟,并与用拉格朗日微分方程处理的模型进行了对比分析,从而验证了所提方法的有效性.

关键词:

刚体系统|动力学|优化问题|广义坐标|高斯最小拘束原理

Abstract:

The purpose of this paper is to study the optimization method for problems of rigid body dynamics systems based on the Gaussian principle of the least constraint in generalized coordinates. Compared to the current modeling methods with the Gaussian principle of the least constraint in the form of the particles, it is shown that modeling the Gaussian principle of the least constraint in generalized coordinates has no requirements upon the coordinates, and the modeling process becomes easy and versatile. Two different optimization models are established in this paper under constrained and unconstrained conditions in the example of a double pendulum. A dynamical numerical simulation and a comparative analysis are carried out with a model treated with the Lagrange differential equation using a software MATLAB and the effectiveness of the method proposed in this paper is verified.

Key words:

rigid system|dynamics|optimization|generalized coordinates|Gaussian principle of least constraint

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