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机械多体系统碰撞动力学的对称性和守恒量研究

郑明亮 冯鲜 李文霞 曹亚玲

郑明亮, 冯鲜, 李文霞, 曹亚玲. 机械多体系统碰撞动力学的对称性和守恒量研究[J]. 应用数学和力学, 2018, 39(11): 1292-1299. doi: 10.21656/1000-0887.380291
引用本文: 郑明亮, 冯鲜, 李文霞, 曹亚玲. 机械多体系统碰撞动力学的对称性和守恒量研究[J]. 应用数学和力学, 2018, 39(11): 1292-1299. doi: 10.21656/1000-0887.380291
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
Citation: 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

机械多体系统碰撞动力学的对称性和守恒量研究

doi: 10.21656/1000-0887.380291
基金项目: 江苏省高等学校自然科学基金(18KJB460027)
详细信息
    作者简介:

    郑明亮(1988—),男,讲师,博士(通讯作者. E-mail: zhmlwxcstu@163.com).

  • 中图分类号: TH122;O316

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

  • 摘要: 为给复杂机械多体系统碰撞动力学问题的定量和定性分析提供一个强有力新工具,该文将现代分析力学中的对称性理论引入到机械多体外碰撞动力学研究中.首先,基于冲量动量法推导系统碰撞动力学的Euler-Lagrange方程;其次,引进群分析理论,根据不变性原则给出系统存在Noether对称性与Lie对称性的各自条件方程以及得到相应守恒量的形式,为动力学方程的解析积分理论提供了有效途径.最后以一平面开环两连杆机构的碰撞力学为例进行实际分析运用.研究表明,借助对称性和守恒量可以得到机械多体系统动力学更深层次的力学规律和运动特性,可为系统更精确的动态优化设计和先进控制奠定理论基础.
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出版历程
  • 收稿日期:  2017-11-21
  • 修回日期:  2018-03-17
  • 刊出日期:  2018-11-01

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