When a cat falls down from a certain height, its four paws are always the parts of its body that touch the ground first. If being tossed up and twisted in the air, the cat always manages to land on its feet. What principals of dynamics does the cat employ to perform this trick? What body parts of the cat get involved in doing this acrobatic performance?

When I was a kid, I owned a cat, and these questions had popped up before, yet I'd never actually had an answer for them. This was a chance for me to really spent time to look for the answers. And it was the reason that compels me to choose this topic for the web project although I knew ahead of time that I would encounter difficulty in finding enough information. Besides, the answers for the above questions would not be simple because the cat body is not a rigid body, but it's very flexible, and every point on that body moves differently at every instant. This made the problem more challenging for me.
Let's consider a cat at the beginning of its fall, when it's up side down. Its four paws are pointing upward and its back is falling toward the ground. At this very instant the only external force acting on this body is gravity, which is in the vertical direction. What the cat needs is an external force in other direction or a torque to turn its body around, so its paws would point toward the ground. However, these force and torque do not exist.
The cat then creates an internal moment by twisting its body muscles. And just like a skater pulling in her arms at a spin in order to increase the angular velocity of her body, the cat simultaneously pulls in its front paws as it twists its body. According to the equation:

Int(M_c)dt = dH_c = d(I_c*w)

The net moment is constant, but the angular inertia (I) is reduced; therefore, the angular velocity (w) increases. In this case, the front angular inertia (I_front) of the cat is reduced, but the rear angular inertia (I_rear) is not. And because its body is flexible, the angular velocity of the front of the cat is higher that of its rear. At this instant, the rear paws of the cat are still pointing toward the sky while his front paws are rolling downward.
Because of gravity, the cat is also falling closer to the ground. Instinctively, he reaches out his front paws again, getting ready to land. As he does so, he increases I_front, and consequently reduces his front angular velocity. When he reaches out his front paws, he also pulls in his rear paws. Conversely, his (I_rear) decreases, and his rear angular velocity increases. Therefore, his rear paws catch up with his front paws. Now all four feet of the cat are pointing downward, and the cat is ready to land.

Of course, the cat may experience a more complicated, twisting fall than being presented, but through thousands of generations of practicing, the cat can easily gain its orientation in the air and controls how much and how fast he should twist his body and pull or extend his legs to achieve the right angular velocities for his body.

There is also a myth saying that the tail of the cat plays an important role in helping the cat landing upright. However, this is not necessarily true because tailless cats can perform this trick perfectly well, too. To the best of my knowledge, the tail helps the cat keep its balance when jumping, running, and chasing preys. It acts as a counter weight when the cat makes a sharp turn at high speed. The tail may influence the landing in some way but not the deciding factor of the cat's ability to land on its feet.

So far, humans have not been able to copy this ability of the cat. It would be wonderful if we can create the landing gears for air crafts to land like cats, or the landing gears for space crafts to safely land on other planets where runways are not available.

Even though our technology is very advanced, we still have a lot to learn from animals and their abilities. As I worked on this project, I found out that things around us are not yet perfect, and they still need to be improved. With thinking and imagination we can step closer to be able to do things that the cats, the fish, or the birds can.
Because of the scarcity of information about this topic, I couldn't find any reference. Most of what I knew came from consulting with Dr. Lipkin, and observation. The hypothesis above about how a cat lands may not be entirely correct. If you do know or find out more about this topic, I would gladly like to learn from you.
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