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Painlevé 疑难的理论分析和实验验证

赵振 刘才山 陈滨

赵振, 刘才山, 陈滨. Painlevé 疑难的理论分析和实验验证[J]. 力学学报, 2013, 45(1): 37-44. doi: 10.6052/0459-1879-12-316
引用本文: 赵振, 刘才山, 陈滨. Painlevé 疑难的理论分析和实验验证[J]. 力学学报, 2013, 45(1): 37-44. doi: 10.6052/0459-1879-12-316
Zhao Zhen, Liu Caishany, Chen Bin. THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 37-44. doi: 10.6052/0459-1879-12-316
Citation: Zhao Zhen, Liu Caishany, Chen Bin. THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 37-44. doi: 10.6052/0459-1879-12-316

Painlevé 疑难的理论分析和实验验证

doi: 10.6052/0459-1879-12-316
基金项目: 国家自然科学基金(11172019, 11132001) 和“凡舟”青年科学基金(20110501)资助项目.
详细信息
    通讯作者:

    赵振

  • 中图分类号: O313

THEORETICAL ANALYSIS AND EXPERIMETNAL VERIFICATION FOR PAINLEV碋 PARADOX

Funds: The project was supported by the National Natural Science Foundation of China (11172019, 11132001) and Fanzhou Youth Research Foundation (20110501).
  • 摘要: 含摩擦的多体系统可能存在Painlevé 疑难奇异性—— 多体系统的后续运动可能存在无解(非协调状态)或者多解(不确定状态). 实际系统总要运动下去, 而对应于非协调奇异性状态的多体系统将经历怎样的运动值得探讨. 从计算、实验和理论证明3 个角度研究Painlevé 疑难问题, 验证和证明了多体系统处于非协调状态时其后续运动的切向冲击特征, 并揭示了切向冲击运动的共同规律.

     

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    2 Brogliato B. Nonsmooth Mechanics, Models, Dynamics and Control. London: Springer-Verlag London Limited, 1999
    3 姚文丽, 徐鉴. 考虑奇异性的平面多刚体系统冲击问题理论解. 振 动工程学报, 2009, 22(1): 65-69 (Yao Wenli, Xu Jian. Theoretical dynamical impact solution on planar multi-rigid-body systems considering singularity. Journal of Vibration Engineering, 2009, 22(1):65-69 (in Chinese))
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    9 Liu CS, Zhen Z, Chen B. The bouncing motion appearing in a robotic system with unilateral constraint. Nonlinear Dynamics,2007, 49 (1-2): 217-232  
    10 Zhao Z, Liu CS, Ma W, et al. Experimental investigation of the Painlevé paradox in a robotic System. J Appl Mech, 2008, 75(4):041006  
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  • 被引次数: 0
出版历程
  • 收稿日期:  2012-11-09
  • 修回日期:  2012-11-21
  • 刊出日期:  2013-01-18

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