How falling cats always land on their feet

Settled in 1969 by T.R. Kane & M.P. Scher.

How a cat dropped upside down with no initial spin manages to land on its feet puzzled scientists since Etienne-Jules Marey's 1894 chronophotographic sequences proved the cat reorients itself in mid-air without violating physics. The apparent paradox - zero angular momentum yet a net 180-degree turn - was resolved qualitatively by recognizing that a non-rigid body can change orientation through shape changes alone, but a full quantitative dynamical model came from Thomas Kane and M.P. Scher's 1969 paper, funded partly by NASA's interest in astronaut self-righting in zero gravity, using a two-rigid-segment model that matched high-speed film data.

A falling cat with zero angular momentum still manages to turn itself right-side-up purely by changing its own shape in mid-air, the same geometric-phase trick a diver or gymnast uses to twist without pushing off anything.

Explanations that circulated

• The cat's self-righting was sometimes claimed to violate conservation of angular momentum; it does not - the cat achieves zero net rotation of overall angular momentum by alternately bending and twisting its front and back halves, with each half's twist compensated by the other plus changes in effective moment of inertia.
• Early qualitative accounts described the cat as reorienting with no clear mechanical model of how a limbless free body could turn itself, until Kane & Scher provided rigorous equations of motion using a two-segment bend-and-twist model.

References

• A dynamical explanation of the falling cat phenomenon90086-9), T. R. Kane, M. P. Scher, International Journal of Solids and Structures, 1969