How can I use Mathematica to write a system of N coupled equations as explicit functions

I have a system of coupled equations from a non-linear mechanical system. My system of equations (as shown below) has two angular acceleration terms. I would like to write down my system as two explicit functions of the two angular acceleration terms.

I don’t have any prior background in using computers for algebraic manipulation or Mathematica in general, but I was informed I might find Wolfram Mathematica useful. I have gone through the documentation but I haven’t been able to find what I’m looking for.

How do I go about doing this?

Thanks! Is there any way I can get a non-numerical solution?

You can get the answer if you ask the question on this webpage

Regards M.I.