Cascadeur: The Problem of the Falling Cat

Everyone knows that a cat always lands on 4 legs, no matter how it is thrown. This question has long been occupied by physicists, and several models have been proposed for how this cat succeeds. All these models are approximate and are usually limited to cylinders. However, the team at Cascadeur's physics-based animation program tried to simulate a cat flip on a more detailed physical model.

Physicists used to think that a cat can calculate its rotation in advance and, at the beginning of a fall, manages to push correctly, acquiring the initial angular momentum. But experiments showed that even if the cat is suspended by the paws on the ropes, and then sharply cut them, the cat still manages to roll over.

Apparently, this is a special reflex in cats - they unconsciously make the correct movement when they lose support and are oriented in space incorrectly. True, in zero gravity this reflex gives a glitch :) But even in zero gravity it is clear that cats can change their orientation in space with their movements.

We decided to try playing this cat trick in Cascadeur. Our physical model of a cat allows us to simulate its movement in sufficient detail.



The main problem with turning cats around is that without pivot points, the cat cannot change its angular momentum . If initially the angular momentum is zero, then it will remain zero further.

We used to think that cats are turning at the expense of the tail - they twist the tail in one direction, and because of this, the body rotates in the opposite direction, keeping the total angular momentum zero. This is a logical idea, but it seems that one tail is not enough - videos of real experiments show that cats do something more complicated. Moreover, a cat can roll over without a tail at all.

It turns out that physicists at different times offered different solutions to this problem.

For example, in 1894, L. Lekorn proposed a model in which a cat consists of two cylinders that rotate at an angle to each other. This was hardly noticed by the scientific community, but later this idea in 1935 was developed by the Dutch researchers Rademaker and Braque.

In experiments, it is noticeable that the cat bends the torso in the middle. You can imagine the front and rear halves of a cat's body as two cylinders that can rotate along their axes. If there is an angle between the axes of the cylinders, then turning them along their axes will create a general compensation rotation in the opposite direction so that the total angular momentum remains zero.

We tried to reproduce this with our saber-toothed cat in Cascadeur.



But no matter how we bend the body, we could not achieve a 180-degree turn. For one such movement, the cat cranked a maximum of 120 degrees. We came to the conclusion that this movement alone is not enough.

Also popular among physicists is the model proposed by M. Guillau, taking into account the tightening of the paws. If you first press the front legs, extend the rear legs, and turn the front half of the body along the axis relative to the rear half, then due to the difference in the moments of inertia, the front half will turn more than the back half will turn in the opposite direction. After that, it is possible to tighten the hind legs, extend the front legs, and rotate the rear half of the body relative to the front, returning to the initial state, then the rear half will turn more than the front, and the final position of the cat will be rotated, despite the fact that the total angular momentum has always remained zero .

This model seems logical, but the important question remains: why does a cat usually stretch only one front and one hind legs, although it would be more profitable to stretch two front and then two hind legs at once?

Carefully studying the video, we noticed that the cat does not just extend one front paw and one hind leg, but rakes them in opposite directions.

Our physical model is more detailed than just two solids. In it you can reproduce the complex movement of the paws.

Having experimented with this raking of paws, we received an unexpectedly strong contribution of this movement of paws to the coup of a cat. If you use body bending plus raking paws, then this is enough for the cat to turn around 180 degrees or more.







In the experiment, we almost did not use the tail, since our saber-toothed cat has a very small tail. But in life, cats rake their feet a little less and bend the body less, and part of the coup really provide the tail.

In total, we came to the conclusion that cats use several principles at once. The bend of the body has the greatest contribution, in second place in the contribution is the raking by the paws, and the tail also helps.

Maybe our experiments are not drawn to scientific work, but we hope that you were interested and you better understand how the cat succeeds in this trick. We will be happy to answer questions in the comments.

Learn more about Cascadeur:

Cascadeur: the future of gaming animation
Cascadeur: prediction character poses on six points

in Banzai Games team require Senior Unity Developer. Read more about the vacancy here .