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

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Abstract

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.

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Acknowledgments

Here, we show thanks and appreciations sincerely to Professor Jie Tian of Hefei University of Technology (China) for his instructions and help during the process of research. The research is supported by the National High-tech Research and Development Program of China (863 Program: 2012AA112201).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Shengchao Zhen & Kang Huang

  2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Han Zhao & Ye-Hwa Chen

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  1. Shengchao Zhen
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  2. Kang Huang
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Correspondence to Shengchao Zhen.

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Zhen, S., Huang, K., Zhao, H. et al. Why can a free-falling cat always manage to land safely on its feet?. Nonlinear Dyn 79, 2237–2250 (2015). https://doi.org/10.1007/s11071-014-1741-2

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  • DOI: https://doi.org/10.1007/s11071-014-1741-2

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