Why can a free-falling cat always manage to land safely on its feet?
- 593 Downloads
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.
KeywordsFree-falling cat Udwadia–Kalaba formulation Equation of motion
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).
- 2.Batterman, R.W.: Falling cats, parallel parking, and polarized light. Stud. Hist. Philos. Mod. Phys. 129, 1–40 (2003)Google Scholar
- 5.Dirac, P.A.M.: Lectures in Quantum Mechanics. Yeshiva University, New York (1964)Google Scholar
- 8.Guyou, E.: Note Sur Les Approximations Numeriques. Kessinger Publishing, Montana (1891)Google Scholar
- 10.Kane, T.R.: Dynamics of nonholonomic systems. J. Appl. Mech. 28(4), 574–578 (1961)Google Scholar
- 12.Kane, T.R.: Dynamics, 3rd edn. Stanford University, Stanford, CA (1978)Google Scholar
- 13.Kane, T.R., Levinson, D.A.: Multibody dynamics. J. Appl. Mech. 50, 1071–1078 (1983)Google Scholar
- 14.Kane, T.R., Levinson, D.A.: Dynamics: Theory and Application. McGraw-Hill, New York (1985)Google Scholar
- 15.Lagrange, J.L.: Mechanique Analytique. Mme ve Courcier, Paris (1787)Google Scholar
- 16.Liu, Y.Z.: On the turning motion of a free-falling cat. Acta Mech. Sin. 4, 388–393 (1982) (In Chinese)Google Scholar
- 17.Loitsyansky, A.I.: Theoretical Mechanics. Saint Petersburger, Moscow (1953)Google Scholar
- 18.Marey, M.: Méchanique Animale. La Nature 119, 596–597 (1894)Google Scholar
- 19.McDonald, D.A.: How does a cat fall on its feet? New Sci. 7, 1647–1649 (1960)Google Scholar
- 20.Montgomery, R.: Gauge theory of the falling cat. Am. Math. Soc. 1, 193–218 (1993)Google Scholar
- 30.Zhen, S.C., Zhao, H., Huang, K., Chen, Y.H.: On Kepler’s law: application of the Udwadia–Kalaba theory. Sci. Sin. Phys. Mech. Astron. 44(1), 24–31 (2014) (in Chinese)Google Scholar
- 31.Zhong, F.: A two-rigid-body model of the free-falling cat. Acta Mech. Sin. 17, 1 (1985)Google Scholar