A disk of smaller diameter and low density displays chaotic motion
, swinging back and forth more and more widely until it flips over, tumbles, then returns to an oscillating mode.
However, the situation is somewhat different for a stadium-shaped cavity -- or a rectangular cavity containing a large disk, which also gives rise to chaotic motion
occurs at intermediate speeds, close to the 6.
Several years earlier, Wisdom and Sussman had found a chaotic motion
for Pluto when they used a different custombuilt computer to solve the differential equations modeling the motion of the outer planets from Jupiter to Pluto.
But to get it to that point, where control of the chaotic motion
becomes possible, researchers normally have to wait until the chaotic system's motion, as depicted by its attractor, happens to land near the desired point.
In a few seconds, the ribbon's chaotic motion
settles into a repeating pattern: first a deep bow, then a nod, then another deep bow, a nod and so on.
Over the past 8 billion years, the galaxies lose chaotic motions
and spin faster as they develop into settled disk galaxies.
The flows we observe in the lab of waters with different densities have the opposite effect: Mixing generates kinetic energy, and the seemingly chaotic motions
of mixing become organized into currents that flow uphill.
The object is in a large, star-forming region where chaotic motions
and eddies in the gas and dust result in smaller cloudlets that can rotate in different directions.