Frustration & Perpetual Motion

Momentum conservation (or Newton’s third law) ensures two-way or bidirectional coupling for typical media like guitar strings and spring mattresses. One-way or unidirectional coupling enables the propagation of solitary waves or solitons with diverse behaviors in otherwise dissipative media, but at the expense of both momentum and energy conservation. Nevertheless, one-way media are possible, provided the coupling is powered to conserve overall momentum and energy.

We recently published an article in Chaos describing the design, construction, and dynamics of low-cost mechanical arrays of 3D-printed bistable elements whose shapes interact with wind to couple them one-way. Periodic boundaries enable solitons to annihilate in pairs in arrays with an even number of elements. Solitons propagate indefinitely in odd arrays that frustrate pairing.

Topological frustration and the power of invisible wind ensure perpetual motion, as in the video below. The mechanical analogue of an electronic ring oscillator of inverting NOT gates, the one-way array is a mechanical clock whose ticks are the reversals of its bistable elements. The design, development, and construction of the array involved five undergraduate co-authors and incorporated two Wooster yearlong senior thesis projects and one NSF REU summer project.

Wind blows down, soliton move right. Each bistable element and the gears were 3D printed in nylon plastic.

Wind blows down, soliton move right. Each bistable element and the gears were 3D printed in nylon plastic. The parity (odd) of the array guarantees perpetual motion.

About John F. Lindner

John F. Lindner was born in Sleepy Hollow New York and educated at the University of Vermont and Caltech. He is a professor of physics and astronomy at The College of Wooster. He has enjoyed multiple yearlong sabbaticals at Georgia Tech, University of Portland, University of Hawai'i, and North Carolina State University. His research interests include nonlinear dynamics, celestial mechanics, and variable stars.
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