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

摘要

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.