WHEN IS CUTTING CHAOTIC

An extended analysis of the cutting model analyzed by Grabec, a four d imensional non-linear dynamical system, shows that there is but one fi xed point, which is unstable for reasonable values of damping. A calcu lation of the Lyapunov exponents and dimension shows that the model sy stem is chaotic for a range of cutting forces, and non-chaotic otherwi se. 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. (C) 1995 Academic Press Limited