How can I get the mathematical model of the surface of a liquid rotating on a inclined surface? So I was playing around with my lab equipment, and I saw that if I let water rotate like this:

It seems that the motion of the surface is periodic.How can I calculate an equation for the motion of the surface?
(The surface was about 5 degrees inclined and the angular velocity was about 4 rad/s)
 A: I very much doubt that there is an analytic solution to the motion of the water. The periodic effect would appear to be the result of resonance when the frequency of rotation is similar to the 'slop' frequency of the tank that can be observed if you gently oscillate a partially filled tank from side to side. You could confirm that by manually wobbling the stationary and level tank to find the frequency where it slops the most, and then trying to rotate it at about that speed to see if that maximized the periodic motion you are observing. If you played with tanks of varying dimensions you might find a linear relationship between maximal-slop frequency and maximal-rotational-slop-frequency.
The effect would probably be 'simplest' with a round tank - but even there I doubt that an exact analytic solution exists. But a rectangular tank will complicate the motion significantly, as there will be more than one slop frequency, and the corners of the tank will 'stir' the liquid in unpredictable ways.

