Question: How I can write a set of nonlinear coupled ODEs in a Matrix form like "Mq"+Cq'+Kq=F", This ODEs are derived from PDEs using Galerkins method

I have a set of nonlinear and coupled PDEs for a cable actuated system. I want to transfer this set to a set of ODEs and write it down in Matrix form. I used Galerkin's method and derived the ODEs in discritized form. I have a problem in converting this set of equation into a matrix form like "Mq"+Cq'+Kq=F". The derived equations are very complicated and contains some nonlinear terms. One of the three equations looks like this:

 

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