Mathieu equation

[mad...@iiitd.ac.in]

I am working on the stability of an inverted pendulum with oscillating base. I have come across of solution by converting it to Mathieu equation. There exist variations in the Mathieu equation which are as follows

1. http://www2.math.ou.edu/~npetrov/joe-report.pdf

2. http://en.wikipedia.org/wiki/Mathieu_function 

I am trying to figure out if there is a correspondence between these equations or they are entirely different.

Please help me if you have any idea about it.

Thanks in advance for the reply.