We’d be “left with” the left hand side of our newton system of course! Eh hem, That was a computational joke. I know, I know, but anyway, build a Newton’s met

We’d be “left with” the left hand side of our newton system of course! Eh hem, That was a computational joke. I know, I know, but anyway, build a Newton’s method for your physics, and the physics is all in the residual (right hand side) with the left hand side purely there to drive it to zero.