I'm trying to find the equation of motion for the system below.
As you see, there is a trailer connected to a car with a spring. There are a "b.v" force where b representing a coefficient of road and internal friction of vehicles. l is not written here, it is the length of the spring at equilibrium.
What I have done so far?
$$
m_{1} \ddot{x_{1}} = u_{1} – b_{1} \dot{x_{1}} – k (x_{1} – x_{2} + l) – b_2 \dot{x_{2}}
$$
$$
m_{2} \ddot{x_{2}} = – k (x_{1} – x_{2} – l) – b_2 \dot{x_{2}}
$$
I don't know if I'm on the right track, any help will be appreciated.
Best Answer
I would write smth like this. The forces acting on the car are: $u_1, F_{friction}^{car}, F_{spring}$ and that is it. The forces acting on the trailer are: $F_{spring}, F_{friction}^{trailer}$, so the equations of motion are
$$m_{1} \ddot{x_{1}} = u_{1}-F_{friction}^{car}-F_{spring} $$ $$m_2 \ddot{x_{2}}=F_{spring}-F_{friction}^{trailer}.$$