The Prüfer Transformation

System (2) can be converted to polar coordinates by setting

and

. With respect to t, differentiate

and

, to obtain

Because equations (6, 7) are partially uncoupled, we can first deal with (6) in isolation to analyze the behavior of , then use our results in equation (7) to examine the amplitude of the function .

Analyzing for the Airy equation.

Contents Next: Analyzing

for the Up:A New Look at Previous: The Airy Equation