string parsing / regexp question

[Ryan Krauss]

I need to parse the following string:

$$\pmatrix{{\it x_2}\cr 0\cr 1\cr }=\pmatrix{\left({{{\it m_2}\,s^2
 }\over{k}}+1\right)\,{\it x_1}-{{F}\over{k}}\cr -{{{\it m_2}\,s^2\,F
 }\over{k}}-F+\left({\it m_2}\,s^2\,\left({{{\it m_2}\,s^2}\over{k}}+1
 \right)+{\it m_2}\,s^2\right)\,{\it x_1}\cr 1\cr }$$

The first thing I need to do is extract the arguments to \pmatrix{ }
on both the left and right hand sides of the equal sign, so that the
first argument is extracted as

{\it x_2}\cr 0\cr 1\cr

and the second is

\left({{{\it m_2}\,s^2
 }\over{k}}+1\right)\,{\it x_1}-{{F}\over{k}}\cr -{{{\it m_2}\,s^2\,F
 }\over{k}}-F+\left({\it m_2}\,s^2\,\left({{{\it m_2}\,s^2}\over{k}}+1
 \right)+{\it m_2}\,s^2\right)\,{\it x_1}\cr 1\cr

The trick is that there are extra curly braces inside the \pmatrix{ }
strings and I don't know how to write a regexp that would count the
number of open and close curly braces and make sure they match, so
that it can find the correct ending curly brace.

Any suggestions?

I would  prefer a regexp solution, but am open to other approaches.

Thanks,

Ryan