A physicist and his cat ‘unravel’ the cat’s equation of motion

In the age of social media, there is no doubt who the animal star is. Cats rule the screens like their cousins, the lions, rule the savannah. Thanks to Erwin Schrödinger, this spear also has an honorable place in the history of physics. And it was Eme the cat that inspired Anxo Biasi, a researcher at the Instituto Galego de Física de Altas Enerxías (IGFAE), to publish an article in American Journal of Physics.

In this paper, Anxo presents the equation of motion for a cat. “This article aims to bring physics closer to non-specialists, to provide an interesting example through which it is possible to understand several concepts of classical mechanics. To do so, an equation is created that shows the behavior of a cat in front of a person, taking the former as a fraction of a point that moves with a force driven by a person,” he summarizes.

Explaining physics and cats

Anxo has recently joined the IGFAE, a joint institution of the University of Santiago de Compostela (USC) and the regional government from Galicia (Spain), through the Junior Leader Program La Caixa, in the Physics Department of the École Normale Supérieure de Paris.

At the IGFAE, where he has completed his doctoral thesis, he will develop his research method on the nonlinear equations of evolution, at the intersection between physics and mathematics, joining the Theory of String and set of related fields.

The idea for the title came down to “discussing physics in a fun way, making it interesting to students,” he says. And so, what seemed, to some extent, as a joke, slowly took the form of a lesson.

“This started as a play idea for Fool’s Day, inspired by funny papers produced by other researchers. However, I soon realized that this story I made could be very useful physics students. This story has a lot of ideas, but it does it in a fun way using an example that arouses great interest: the cat!”

And how is the equation of motion for cats constructed?

Anxo starts from seven energies, or methods, extracted from his daily experience with Eme, and uses the theory that “cats behave as if they see the energy around a person.”

In this way, the article states that the seven dynamics mentioned above can be modeled, as a first measure, by considering the cat as a particle of point obeying Newtonian mechanics.

The cat has “power” relative to the external force (induced by the presence of the person) where x

Starting from this formula, and by analyzing the movement of cattle, it is possible to show how the equations themselves are constructed.

“This work shows, in an interesting way, the mental process that was followed in the creation of physics models, which are often described in detail in the literature. For example, moving (or stationary) systems is checked, it comes from the fact that cats tend to walk. They don’t come when called, they are easily interrupted, or they stay for a long time in the lap of the person they love.”

All these figures are approached in an engaging and fun way. “We don’t always need to deal with the deepest and most difficult mysteries of the universe; sometimes we can relax and use the power of physics to explain everyday life – it’s really funny!” , Anxo says.

In this way, “the cat-human interaction model brings physics closer to non-specialists, showing in a curious and familiar way the reason for the construction of physical models,” he sums up.

Review of purring and zoomies

The paper focuses on the characteristic analysis of the feline purr. His suggestion is that this response is a stabilizing mechanism, fueled by the interaction between the cat and its human partner.

“It is suggested that when a cat is stroked and begins to purr, people tend to feel motivated to continue petting it, thus enhancing the stability of the process.”

This stability is also strengthened by the fact that the exchange of affection between purring and stroking temporarily strengthens the bond between the cat and the person.

The study also looks at random episodes, known as FRAP or “zoomies,” when cats move at full speed from one location to another, often at night. The paper talks about how, in this case, the equation needs an unpredictable part to model these moments, which is built in a way like “forcing” from the outside. This adds another dimension needed to model a cat’s “explosion”, which to some extent can be adjusted to individual specifications.

Use of education

In addition to its playful approach, Anxo emphasizes that this article “is intended to be used in introductory courses in classical mechanics, to show how seemingly complex and unrelated behavior can be explained by simple rules.”

It does so by showing “a series of dynamics that are easy to visualize, reducing the need for abstraction,” and provides a “differential equation, which covers the foundations of ancient machinery.”