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We begin our discussions with an example which illustrates the wide range of problems to which the techniques discussed in this book may be applied. The methods we develop as we proceed are quite general and apply to the analysis of time series observations of physical or other systems. The example we have chosen to start the development is comprised of observations of chatter in machine tool production. This is really quite far afield from what one is accustomed to encounter on opening a book on nonlinear dynamics and chaos. I have chosen this example both because it strays from that path and for its intrinsic importance and interest. I ask the reader whose interest in machine tools may be quite minimal to think of this example as illustrative of how one can systematically proceed with the analysis of observed irregular data. It also illustrates important issues about chatter and may have substantial application in terms of making better milling machines. This potential is only one goal of the example.
KeywordsMachine Tool Lyapunov Exponent Average Mutual Information Tool Holder Large Lyapunov Exponent
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