@MASTERSTHESIS\{IMM2004-03224,
    author       = "B. Gilles",
    title        = "Nonlinear railway vehicle dynamics",
    year         = "2004",
    keywords     = "Nonlinear dynamics, chaos, Lyapunov exponents, bifurcations, railway dynamics, dry-friction, stick/slip.",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by Assoc. Prof. Hans True",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/3224-full.html",
    abstract     = "We investigate the motion of a railway vehicle travelling along a straight track, with constant rolling velocity v. The model contains dry-friction dampers which introduce a stick/slip effect. We consider only three degrees of freedom, so that the impact of the stick/slip phenomenon can be more clearly detected. The dynamics are described by a nonlinear system of equations obtained by applying classical mechanics laws.

The behaviour of the solutions turns out to be highly sensitive to the parameter v, as a complex sequence of bifurcations occurs all across the velocity spectrum 5m/s   v   40m/s. Several different types of attractors are found - some are periodic, others are chaotic. We discuss two methods to estimate the largest Lyapunov exponent  y1. The standard method involving Gram- Schmidt orthonormalizations is found to contain large but systematic errors. We therefore present a simple method for estimating these errors, and use the error estimates as correction terms. The resulting estimates of  y1 are used to test for chaotic solutions across the velocity spectrum."
}