Algorithm for Rolling Down in the Desired Direction

Algorithm for Rolling Down in the Desired Direction
Algorithm for Rolling Down in the Desired Direction

A group of physicists and mathematicians from the Soft and Living Matter Center of the Institute of Basic Sciences in South Korea, in collaboration with a colleague from the University of Geneva, developed an algorithm that can be used to determine the shape of an object so that it will roll down a ramp in the desired direction. .

In their study published in the journal Nature, the group discusses how they built their algorithm and its potential applications. In the same journal, Henry Segerman of the Georgia Institute of Technology and Elisabetta Matsumoto of Oklahoma State University published a News & Views article summarizing the team's work on this new effort.

The team running this new study started with an intriguing conundrum that required imagining a sphere rolling downhill. Considering the sphere is made of clay, it can bend (deform) as it rolls to follow a predetermined path.

The new shape anomalies of the sphere cause it to follow the same path when it rolls down the ramp again. The researchers discovered that, due to an almost infinite number of conceivable deformations, the sphere could go in almost any direction.

After reaching this fact, they began to investigate whether the deformations developing in such a sphere could be mathematically linked to its course. And if that's the case, could such math be used to develop an algorithm that could be used to 3D print a sphere with deformations that would cause it to go a certain route?

It turns out that the answer to both questions is yes. Using mathematical and physical principles, the group developed formulas to determine the deformations that would cause a given object to follow a desired path in an inclined plane. They then developed a computer program that could be used to 3D print such an object in the real world.

The group called these objects orbitals. Each was weighted by a solid metal ball bearing inside. They also discovered that they could produce trajectories that cut a given path twice; They gave the term "two-period orbits" to these orbits.

The research team says the formulas and algorithm they developed could be applied to applications in robotics, physics research involving the angular moment of an electron, or quantum research involving the development of a quantum bit.


📩 13/08/2023 18:30