Abstract: In this article，we give both qualitative and quantitative explanations of why a train stays on itstrack， in spite of

perturbations that could cause it to derail.We show that train stability originatesfrom the conical shape of the

wheels，which gives rise to a restoring normal force in response to alateral disturbance.We first demonstrate translational

stabilization in a simple situation where therails are assumed frictionless and the steering motion of the wheel

is neglected.We then develop amore comprehensive model， taking friction and steering into account.We show that

rolling frictioncouples the rotational motion to the translational motion，enhancing overall stability.Finally，we find

approximate formulae for the parameters governing stability，and show good agreement withparameters of a real railway

coach.