What Is the Name of the Curve Traced by a Ball on a Ripple Wave?

[topito2]

Do you know if there is any name for the equation that describes the shape of a ripple wave? An example of that kind of wave can be found at http://en.wikipedia.org/wiki/Image:Elliptical_trajectory_on_ripples.png.
My question is: what would you call the curve traced by the ball rolling along the ripple wave curve?

 

[Integral]

The best approximation to water surface waves currently in use is a version of the Shcrodinger Wave equation.

Oceanographers often use something called the "linear model" but it fails in extreme cases.

I believe that that path followed by a floating object is nearly an elipsiod.

 

[charng]

The equation that describes the shape of a ripple wave is known as the Laplace equation or the Laplace-Beltrami equation. This equation is a fundamental part of fluid dynamics and describes the behavior of fluids in motion, including ripples on the surface of water.

As for the curve traced by the ball rolling along the ripple wave curve, it would be known as a cycloid. This is a curve that is traced by a point on the circumference of a circle as it rolls along a straight line. In the case of a ball rolling on a ripple wave, the cycloid is formed by the ball's motion along the curved surface of the ripple.

I hope this answers your question and provides some insight into the mathematical principles behind ripple waves.