Stépán, G., 1989, "*Retarded Dynamical Systems: Stability and Characteristic Functions*", John Wiley & Sons, New York.

Insperger, T., and Stépán, G., 2004, “Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay,” Int. J. Numer. Methods Eng., 61 , pp. 117–141.

[CrossRef]Ma, H.Butcher, E. A., and Bueler, E., 2003, “Chebyshev Expansion of Linear and Piecewise Linear Dynamic Systems With Time Delay and Periodic Coefficients Under Control Excitations,”ASME J. Dyn. Syst., Meas., Control, 125 , pp. 236–243.

[CrossRef]Butcher, E., Ma, H., Bueler, E., Averina, V., and Szabó, Z., 2004, “Stability of Linear Time-Periodic Delay-Differential Equations Via Chebyshev Polynomials,” Int. J. Numer Methods Eng., 59 , pp. 895–922.

[CrossRef]Deshmukh, V., Ma, H., and Butcher, E. A., 2006, “Optimal Control of Parametrically Excited Linear Delay Differential Systems Via Chebyshev Polynomials,” Opt. Control Appl. Methods, 27 , pp. 123–136.

[CrossRef]Engelborghs, K., Luzyanina, T., ’T.Hout, K. J., and Roose, D., 2000, “Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations,” SIAM J. Sci. Comput. (USA), 22 , pp. 1593–1609.

[CrossRef]Argyris, J. H., and Scharpf, D. W., 1969, “Finite Elements in Time and Space,” Nucl. Eng. Des., 10 (4), pp. 456–464.

[CrossRef]Borri, M., Bottasso, C., and Mantegazza, P., 1992 “Basic Features of the Time Finite Element Approach for Dynamics,” Meccanica, 27 , pp. 119–130.

[CrossRef]Mann, B. P., Garg, N. K., Young, K. A., and Helvey, A. M., 2005, “Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration,” Nonlinear Dyn., 42 , pp. 319–337.

[CrossRef]Patel, B. R., Mann, B. P., and Young, K. A., 2008, “Uncharted Islands of Chatter Instability in Milling,” Int. J. Mach. Tools Manuf., 48 , pp. 124–134.

[CrossRef]Budak, E., and Altintaş, Y., 1998, “Analytical Prediction of Chatter Stability Conditions for Multi-Degree of Systems In Milling. Part I: Modelling,”ASME J. Dyn. Syst., Meas., Control, 120 (1), pp. 22–30.

[CrossRef]
Merdol, S., and Altintas, Y., 2004, “Multi Frequency Solution of Chatter Stability for Low Immersion Milling,” ASME J. Manuf. Sci. Eng., 126 (3), pp. 459–466.

[CrossRef]Schmitz, T. L., Davies, M. A., Medicus, K., and Snyder, J., 2001, “Improving High-Speed Machining Material Removal Rates by Rapid Dynamic Analysis,” CIRP Ann., 50 (1), pp. 263–268.

[CrossRef]Smith, S., and Tlusty, J., 1991 “An Overview of the Modeling and Simulation of the Milling Process,” ASME J. Eng. Ind., 113 , pp. 169–175.

[CrossRef]Montgomery, D., and Altintaş, Y., 1991, “Mechanism of Cutting Force and Surface Generation in Dynamic Milling,” ASME J. of Eng. Ind., 113 , pp. 160–168.

[CrossRef]Zhao, M. X., and Balachandran, B., 2001, “Dynamics and Stability of Milling Process,” Int. J. Solids Struct., 38 (10–13), pp. 2233–2248.

[CrossRef]Altintaş, Y., and Budak, E., 1995 “Analytical Prediction of Stability Lobes in Milling,” CIRP Ann., 44 (1), pp. 357–362.

[CrossRef]Davies, M. A., Pratt, J. R., Dutterer, B., and Burns, T. J., 2002, “Stability Prediction for Low Radial Immersion Milling,” ASME J. Manuf. Sci. Eng., 124 (2), pp. 217–225.

[CrossRef]Minis, I., and Yanushevsky, R., 1993, “A New Theoretical Approach for Prediction of Machine Tool Chatter in Milling,” ASME J. Eng. Ind., 115 , pp. 1–8.

Insperger, T., and Stépán, G., 2000, “Stability of the Milling Process,” Period. Polytech., 44 (1), pp. 47–57.

Mann, B. P., Bayly, P. V., Davies, M. A., and Halley, J. E., 2004, “Limit Cycles, Bifurcations, and Accuracy of the Milling Process,” J. Sound Vib., 277 , pp. 31–48.

[CrossRef]Insperger, T., Mann, B. P., Stépán, G., and Bayly, P. V., 2003,” Stability of Up-Milling and Down-Milling, Part 1: Alternative Analytical Methods,” Int. J. Mach. Tools Manuf., 43 , pp. 25–34.

[CrossRef]Mann, B. P., Young, K. A., Schmitz, T. L., and Dilley, D. N., 2005, “Simultaneous Stability and Surface Location Error Predictions in Milling,” ASME J. Manuf. Sci. Eng., 127 , pp. 446–453.

[CrossRef]Schmitz, T. L., and Mann, B., 2006, “Closed Form Solutions for the Prediction of Surface Location Error in Milling,” Int. J. Mach. Tools Manuf., 46 , pp. 1369–1377.

[CrossRef]Butcher, E., Bobrenkov, O., Bueler, E., and Nindujarla, P., 2009, “Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels,” ASME J. Comput. Nonlinear Dyn., 4 (3), p. 031003.

[CrossRef]Bobrenkov, O., Khasawneh, F., Butcher, E., and Mann, B., 2010, “Analysis of Milling Dynamics for Simultaneously Engaged Cutting Teeth,” J. Sound Vib., 329 (5), pp. 585–606.

[CrossRef]Tobias, S. A., 1965, "*Machine Tool Vibration*", Blackie, London.

Tlusty, J., and Polacek, M., 1963, "*“The Stability of Machine Tools Against Self-Excited Vibrations in Machining,”*"*Proceedings of the ASME International Research in Production Engineering*, Pittsburgh, PA, pp. 465–474.

Merrit, H. E., 1965, “Theory of Self-Excited Machine-Tool Chatter,” ASME J. Eng. Ind., 87 (4), pp. 447–454.

Davies, M., Pratt, J., Dutterer, B., and Burns, T., 2000, “The Stability of Low Radial Immersion Milling,” CIRP Ann., 49 (1), pp. 37–40.

[CrossRef]Bayly, P. V., Halley, J. E., Mann, B. P., and Davis, M. A., 2003, “Stability of Interrupted Cutting by Temporal Finite Element Analysis,” ASME J. Manuf. Sci. Eng., 125 , May, pp. 220–225.

[CrossRef]Insperger, T., Stépán, G., Bayly, P. V., and Mann, B. P., 2003, “Multiple Chatter Frequencies in Milling Processes,” J. Sound Vib., 262 , pp. 333–345.

[CrossRef]Mann, B. P., Insperger, T., Bayly, P. V., and Stépán, G., 2003, “Stability of Up-Milling and Down-Milling, Part 2: Experimental Verification,” Int. J. Mach. Tools Manuf., 43 (1), pp. 35–40.

[CrossRef]Balachandran, B., 2001, “Non-Linear Dynamics of Milling Process,” Proc. R. Soc. London, Ser. A, 359 (1781), pp. 793–819.

[CrossRef]Insperger, T., Muñoa, J., Zatarain, M., and Peigné, G., 2006, “Unstable Islands in the Stability Chart of Milling Processes Due to the Helix Angle,”"*Proceedings of CIRP Second International Conference on High Performance Cutting*", June 12 and 13, CIRP, Vancouver, Canada.

Zatarain, M., Muñoa, J., Peigné, G., and Insperger, T., 2006, “Analysis of the Influence of Mill Helix Angle on Chatter Stability,” CIRP Ann., 55 , pp. 1–4.

[CrossRef]Mann, B., Edes, B., Easley, S., Young, K., and Ma, K., 2008, “Chatter Vibration and Surface Location Error Prediction for Helical End Mills,” Int. J. Mach. Tools Manuf., 48 , pp. 350–361.

[CrossRef]Altintaş, Y., 2000, "*Manufacturing Automation*", 1st ed., Cambridge University Press, New York.

Martelloti, M. E., 1941, “An Analysis of the Milling Process,”Trans. ASME, 63 , pp. 677–700.

Martelloti, M., 1945, “An Analysis of the Milling Process, Part 2: Downmilling,” Trans. ASME, 67 , pp. 233–251.

Mann, B., and Patel, B., 2010, “Stability of Delay Equations Written as State Space Models,” J. Vib. Control, 16 , pp. 1067–1085.

[CrossRef]Khasawneh, F., Mann, B., Bobrenkov, O., and Butcher, E., 2009, “Self–Excited Vibrations in a Delay Oscillator: Application to Milling With Simultaneously Engaged Helical Flutes,”"*Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference*", August 30-September 2, 2009, San Diego, California, paper no. DETC2009-86636.

Khasawneh, F., Patel, B., and Mann, B., 2009, “A State-Space Temporal Finite Element Approach for Stability Investigations of Delay Equations,”"*Proceedings of the ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems*", September 21–23, 2009, Oxnard, California, paper no. SMASIS2009-1263.

Szalai, R., and Stépán, G., 2006, “Lobes and Lenses in the Stability Chart of Interrupted Turning,” ASME J. Comput. Nonlinear Dyn., 1 , pp. 205–211.

[CrossRef]Sims, N. D., Mann, B., and Huyanan, S., 2008, “Analytical Prediction of Chatter Stability For Variable Pitch and Variable Helix Milling Tools,” J. Sound Vib., 317 , pp. 664–686.

[CrossRef]