Abstract
An extended analysis of the cutting model analyzed by Grabec, a four dimensional non-linear dynamical system, shows that there is but one fixed point, which is unstable for reasonable values of damping. A calculation of the Lyapunov exponents and dimension shows that the model system is chaotic for a range of cutting forces, and non-chaotic otherwise. The Grabec model is discontinuous, and it was necessary to replace the discontinuities by sharply varying continuous functions in order to calculate the Lyapunov exponents.
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