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Falling cats and Olympic divers share the ability to twist, spin, and reorient themselves to land on their feet or make minimal splash. To accomplish that feat, they bend and contort to make a complete loop in their body’s “shape space,” so their bodies end up in the same shape they started in. But in physical space, they don’t end up where they started: They rotate through a finite angle. Michael Berry described that acquired rotation, a so-called geometric phase, 35 years ago for quantum systems, and the phase now bears his name. Shortly thereafter, John Hannay extended the concept to classical analogues, for which the iconic example is a bead sliding frictionlessly on a horizontal, rotating, noncircular hoop. After one rotation, the hoop returns to its starting orientation, but the bead will have moved by an angle that depends only on the hoop geometry, not on its rotation speed.

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Category: Science