Although this has indeed "worked to bits" on the Physics and other SE sites it's worth looking at, for the sake of Space Exploration, the interesting history behind the analysis of the falling cat. For the fully rigorous description of the cat's righting reflex - perfectly in keeping with conservation of angular momentum - only came about because it was prompted precisely by research that was done in the late 1950s and early 1960s into how the human body would deal with the environment it met in outer space.
The main researcher here was Professor Thomas Kane, who
- Found the correct theoretical equations describing the cat's shift in orientation in response to its "shape shifting" during the righting reflex;
- Experimentally showed that humans could, with some training, make the righting reflex motions and flip over exactly like a cat.
The primary reference here is:
T. R. Kane and M. P. Scher, “A Dynamical Explanation of the Falling Cat Phenomenon“, Int. J.Solids and Structures, 5, pp663-670, 1969
Indeed Thomas Kane trained people to do this in 1968 in Apollo spacesuits, as shown below.
The left falling cat sequence was taken from the work of physiologist Étienne-Jules Marey (1830-1904) (famous for the development of motion photography for the study of high speed movements); the one on the right was taken during Thomas Kane's 1968 experiments with a trampolinist in an Apollo like spacesuit. Étienne-Jules Marey was a physiologist who did some of the little serious research into the cat's righting reflex before the outer space prompted research of Thomas Kane. Marey, unlike many of his contemporaries, clearly understood that the cat's motion was torque free (see footnote) and indeed used his photography to rule out a commonly held theory that the cat pushes off whatever it falls from. The collage was taken from
Alexis C. Madrigal, “Video: Deducing the Physics of How Cats Fall“, The Atlantic Magazine, 9th September, 2011
Now to clear up some popular misconceptions about the cat righting reflex, particularly applied to astronauts.
The rollover motion is not particularly burdensome or clumsy for humans to do, as Thomas Kane's experiments showed. It's very much like a hula hoop motion. OK so my CGI skills are crap - this is the best cat animation I can make with basic solids in Mathematica, but this movement will roll you over in space, whether you be cat or human, with or without a tail.
The only differences between cat and human for this motion are (1) the cat's spine is much bendier than ours, so that the flipover can be done in fewer "hula hoop" cycles by the cat and (2) the exquisite sensitivity of the cat's vestibular system and lightning swift reflexes compared to ours. Point (2) is irrelevant when one is making a planned rotation in a freefall (gravity free) state in space, as opposed to flipping oneself over in limited time as one falls.
Another common misconception is that the cat needs its tail to flip over: this is wrong as shown by Thomas Kane's experiments that show tailless humans can make the righting motion. Indeed for our housecats, the tail is actually not used much for the reflex at all. I cite here solid observational evidence of my own here: my own cat has been tailless since she was run over by a car in 2004 and has no difficulty whatsoever righting herself when she falls off things, which she does often owing to her somewhat clumsy nature – typically when she falls asleep with her head drooping too far over the edge of our bed. Even though twelve years old, she manages to rouse herself and make the righting reflex within the time it takes her to fall the 40cm or so to the ground from off our bed. Moreover, just after the time she had the accident, I saw her make the righting reflex falling asleep in this way when she had healed barely well enough to walk properly. So it would seem that she needed very little "retraining" to adjust for her new lack of tail. This also comes out of a theoretical analysis, as I show in my article cited below. Indeed the analysis of the video below from Wikipedia, showing the isosceles triangle addition of the two angular momentum vectors is valid only for a "symmetric" cat (owing to the isosceles shape of the vector addition diagram) with no tail (i.e. a cat whose hinder half has the same inertia tensor about the origin as the forward half).
(Source: Wikipedia "Cat Righting Reflex" Page)
Some wild cats, notably the Asian Clouded Leopard and the Asian Marbled Cat have huge tails, much more like a club than the elegant, slender (and very small mass moment of inertia) tail of the housecat (Felis Sylvestris) and this is indeed very much used to control the animal's orientation in space, but the tail lets the animal reorient itself freely about all three axes i.e. it can pitch and yaw as well as roll pretty much at will - in contrast to simply flipping over in the cat righting reflex, which is essentially a one-axis motion. This is a useful ability for tree dwelling predators as they leap from tree to tree and also precision dive-bomb their prey.
I discuss all this in much more detail in my article (including the analysis of "symmetric" (tailless) cats on my website:
"Of Cats and their most Wonderful Righting Reflex"
Footnote: The primary source for Marey's 1894 studies is the following:
Étienne-Jules Marey, “Des mouvements que certains animaux exécutent pour retomber sur leurs pieds, lorsqu’ils sont précipités d’un lieu élevé“, La Nature, 1119, 10 Novembre 1894
Near the end of this article he makes the following definitive statement (translation mine, so apologies to French speakers): "First of all, the inspection of these figures [photos of falling cats] rules out the notion that the animal imparts a rotational motion on itself by thrusting against the hands of the experimenter. [This conclusion follows] because the first frames of the two series [of photos of a falling cat] show that in the first instants of it its fall, the cat as yet has no tendency to turn from one side nor the other. Its rotation only begins with the twisting of its waist."