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Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter
Mathematical Biosciences and Engineering
In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert Wdoi:10.3934/mbe.2007.4.355 pmid:17658931 fatcat:m3lcoew4o5hjvdq5zjdqsz2y4y