Why can a free-falling cat always manage to land safely on its feet?

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• 作者：Shengchao Zhen ; Kang Huang ; Han Zhao ; Ye-Hwa Chen
• 关键词：Free ; falling cat ; Udwadia–Kalaba formulation ; Equation of motion
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：79
• 期：4
• 页码：2237-2250
• 全文大小：782 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

Udwadia–Kalaba equation is a simple, aesthetic and thought-provoking description of the world at a very fundamental level. It is about the way systems of bodies move. We creatively apply the Udwadia–Kalaba approach to study falling cat’s movements. The cat is modeled as a constrained discrete dynamical system. In an alternative way, Udwadia–Kalaba formulation is used for analysis of the falling cat’s dynamics. With this novel approach, we can easily obtain the dynamical model and get the explicit analytic form of the general equations of motion of the falling cat. The surprise phenomenon (that a cat when dropped at rest with its feet pointing up can always manage to right itself and land safely on its feet) is observed through numerical simulation based on the constructed dynamical model. Unmatched ease, clarity and elegance of the Udwadia–Kalaba formulation for solving the falling cat problem (constrained discrete dynamical system or multibody system) are presented.