A Note on the Lyapunov Stability Analysis of a Linear Railway Wheelset

In this paper a Lyapunov function is generated for the linearized equations governing a steel wheelset on steel rails. Thus the authors attack the asymmetric problem, and successfully apply Ingwerson's method for constructing Lyapunov functions. The stability criteria applied to this function yield a closed-form expression for the critical forward speed of the wheelset. Thus the authors retain the advantage of Lyapunov's direct method by obtaining an explicit solution for the critical speed. And, although this linearized result has been obtained by other methods, the result is provocative because it suggests that a similar attack on the intractable nonlinear problem (currently being mounted by the authors) may indeed bear fruit.