Most people are familiar with the acrobatic abilities of cats. One minute their standing on the back of the couch or the kitchen counter, the next, their sliding off, but somehow, despite the unexpected fall, they land square on their feet. The couch, the countertop, even a high shelf, are still no comparison to the tops of a tree or a high balcony. Even at these heights cats can fall or jump and land on their feet. But how?
Physicists have studied the science and math principles of a cat’s ability to land on its feet. For physicists James Clerk Maxwell and George Stokes, they aimed to find out the theory behind the reason why cats are so agile, so at the turn of the 19th century, during their study into this, they threw cats of the window to learn more.
According to Maxwell, he had to explain why he was participating in this seemingly mad experiment. This is what he told her:
“There is a tradition in Trinity that when I was here I discovered a method of throwing a cat so as not to light on its feet, and that I used to throw cats out of windows. I had to explain that the proper object of research was to find how quick the cat would turn round, and that the proper method was to let the cat drop on a table or bed from about two inches, and that even then the cat lights on her feet.”
(The Life of James Clerk Maxwell with extracts from his Correspondence, letter, 1870 p.599)
For Stokes’ daughter, she too thought this sounded like a miserable experiment for cats and had this to say about what her father was doing:
“He was much interested, as also was Prof. Clerk Maxwell about the same time, in cat-turning, a word invented to describe the way in which a cat manages to fall upon her feet if you hold her by the four feet and drop her, back downwards, close to the floor. The cat’s eyes were made use of, too, for examination by the ophthalmoscope, as well as those of my dog Pearl: but Pearl’s interest never equaled that of Professor Clerk Maxwell’s dog, who seemed positively to enjoy having his eyes examined by his master.”
(Memoir and Scientific Correspondence of the Late Sir George Gabriel Stokes, Humphrey, 1907)
Both of these men were very interested in the same thing:
“How does the cat manage to turn around without violating the conservation of angular momentum? The prevailing assumption in the 19th century was that the cat must be using some kind of “push off” from the dropper’s hand.”
In 1894, high-speed photography that was being pioneered by Étienne-Jules Marey, showed quite clearly that there was no push off. And there is no initial rotation from a cat that’s dropped.
The photographs revealed exactly what was happening, however, the pictures still didn’t shed much light on the actual physics of the process. Then, during the course of the 20th century, influential papers dove deeper into the phenomenon. and began taking a closer look.
Physicists Lecornu, Radenaker, Braak, Kane, and Scher, described the events as very intricate. They claim that in order for a cat to keep its total angular momentum at zero the entire time, it does this by sharply bending its body, then it twists each half on two axes that combine to cancel out the rotation of the whole.
It is said that the motion itself is straightforward enough that it can be set up in different equations, however, it is virtually impossible to put the explanation into words. There is a non-technical version of the theory, which you can see on Wikipedia’s animated gif. But for an even clearer explanation you can view, there is a hand-drawn cartoon by Montgomery that makes it simpler to see.
One reason Montgomery’s version is clear to see, is he chose to examine an “extremified” twisting path. In his version, he breaks down the different stages of the cat’s motion and illustrates them in isolated sections. Here they are:
Folding up stage where there is zero angular momentum because both parts are moving in the opposite direction.
There is a rotation of each half in opposite directions. This is another incidence of zero angular momentum since both halves are again, rotating at the same time, just opposite of each other.
The unfold, which is also at zero angular momentum for the very reason you see in the first stage.
Although these stages drawn out were extreme, it does show that on a real cat, although it does this process a bit different, which is that it combines the stages into each other, and this circumvents the need for a complete 180 degree fold.
Montgomery took it a step further and reformulated the whole theory and changed it using terms of a “space” of shapes, which the cat can adopt.
Here’s what is written in R. Montgomery, 1993, Gave more general solutions, showing that Kane and Scher’s solution is the most efficient, and nailed down some surprising links to gauge theories in physics, about Montgomery’s theory:
“To do this, Montgomery reformulates the problem in terms of a “space” of shapes that the cat can adopt, relates this to the overall configuration space for the cat, and imposes a condition that constrains the total angular momentum to zero. He then shows that the reachable states give him a gauge situation (with the anholonomy being the overall rotation of the cat in physical space) and then — apparently for fun — shows that the optimized solution for reaching any given orientation is equivalent to the equations of motion for a charged particle travelling on the projective plane under the influence of an axially symmetric magnetic field and metric.”
All of the physicists theories together, have formed some of the very basics of some of the most influential theoretical work in physics and have helped to better understand how cats land on their feet from high places.