Mathematicians have found a hidden 'reset button' for undoing rotation
a day ago
- #physics
- #mathematics
- #robotics
- Mathematicians discovered a universal method to undo the rotation of nearly any object by scaling and repeating the rotation.
- Jean-Pierre Eckmann and Tsvi Tlusty found that scaling the initial rotation by a common factor and repeating it twice can reset the object's position.
- The method applies to various rotating objects like spins, qubits, gyroscopes, and robotic arms.
- The mathematical proof uses the SO(3) space, which catalogues all possible rotations in three dimensions.
- Undoing a rotation halfway is easier as it corresponds to reaching any point on the surface of the SO(3) space rather than the center.
- The researchers used the 19th-century Rodrigues formula and an 1889 number theory theorem to conclude that the necessary scaling factor almost always exists.
- Potential applications include nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) for undoing unwanted spin rotations.
- The method could also advance robotics, enabling robots to follow repeating paths or morph between shapes for desired movements.