When the Wright brothers pioneered powered flight, said Leif Ristroph, they “didn’t solve a lift problem; they solved a stability problem.”

Dr. Ristroph, who works in applied mathematics at New York University’s Courant Institute, also solved a stability problem recently, with a small, hovering, flapping-wing flying machine that looks for all the world like a flying jellyfish.

The lightweight, electrically powered machine, which seems to be the first of its kind, keeps itself right side up without the benefit of sensors or any righting mechanism. Its stability is completely a result of its shape and the movement of its three-inch wings.

Image The jellyfishlike flying machine. Credit... Leif Ristroph/New York University

As Dr. Ristroph and Stephen Childress, also at the Courant Institute, reported Wednesday in The Journal of the Royal Society Interface, their goal was to create a hovering flyer in a new form — not a helicopter, and not a robot based on reverse engineering insect flight.