I am trying to make a simulator for a car/trailer combination that will allow me to get a rough estimate of trailer dampening and other factors. I have found that many papers suggest simplifying it to a 'tricycle' model, where any given trailer is composed of three wheels.

They then come up with a system of equations and simplify them into matrix form, and furthermore change it to a state equation as seen in the top right and bottom left:

I recognize this form, and they give as inputs. (u would be an active damping which for me is zero. )

Basically, I cannot figure out how to go from this state equation to the what the actual vehicle response it to an input. When I look up state equations usually there is a y component, but I do not appear to have a second equation. I am not sure how to proceed with coding this, or doing it by hand. I am using MATLAB.

Here are the matrix values. Everything listed is a constant, and I can provide the list of the variables if needed. I can't attach the paper, its too large.

Thank you for any assistance you can give me or guidance to other help.