Considering a mass $m$ moving in empty space that is subject to some input force $\textbf{F}$, how would one reach the result that $\textbf{F} = m \textbf{a}$ using Lagrangian mechanics?
Background: I am interested because I want to model a vehicle with wheels. For example, a vehicle with two parallel wheels (like an iRobot). The wheels limit the velocity of the vehicle at each point to not make the wheels go "sideways". I think Lagrangian mechanics provide the easiest method with which to deal with that sort of restriction, by considering the angular position of the wheels as generalized coordinates. I want to apply a torque on one of the wheels in order to accelerate the vehicle. Suggestions for other approaches besides this one are also welcome.
