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ME 629: References

On-line textbook
A free textbook on Nonlinear Vibrations by Richard Rand is available for download.
Perturbation Methods
  • Bender, C.W. and Orszag, S.A., Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, Inc., New York, 1978.
  • Holmes, M.H., Introduction to Perturbation Methods. No. 20 in Texts in Applied Mathematics. Springer-Verlag, New York, 1995.
  • Kevorkian, J. and Cole, J.D., Multiple Scale and Singular Perturbation Methods. No. 114 in Applied Mathematical Sciences. Springer-Verlag, New York, 1996.
  • Nayfeh, A.H., Perturbation Methods. John Wiley & Sons, Inc., New York, 1973.
  • Nayfeh, A.H. and Mook, D.T., Nonlinear Oscillations. John Wiley & Sons, Inc., New York, 1979.
  • Rand, R.H. and Armbruster, D., Perturbation Methods, Bifurcation Theory, and Computer Algebra. No. 65 in Applied Mathematical Sciences. Springer-Verlag, New York, 1987.
Nonlinear Vibrations
  • Jordan, D.W. and Smith, P., Nonlinear Ordinary Differential Equations. Clarendon Press, Oxford, 1987.
  • Meirovitch, L., Methods of Analytical Dynamics. McGraw-Hill, Inc., New York, 1970.
  • Rand, R.H., Topics in Nonlinear Dynamics with Computer Algebra. No. 1 in Computation in Education: Mathematics, Science and *Engineering. Gordon and Breach Science Publishers, Langhorne, Pennsylvania, 1994.
  • Stoker, J.J., Nonlinear Oscillations. Interscience, New York, 1950.
Linear Vibration Theory
  • Kelly, S.G., Fundamentals of Mechanical Vibrations. McGraw-Hill, New York, 1993.
  • Meirovitch, L., Elements of Vibration Analysis. McGraw-Hill, Inc., New York, 1986.
  • Thomson, W.T., Theory of Vibration with Applications. Prentice-Hall, New York, 3rd edn., 1988.
Dynamical Systems
  • Guckenheimer, J. and Holmes, P.J., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. No. 42 in Applied Mathematical Sciences. Springer-Verlag, New York, 1983.
  • Hirsch, M.W. and Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, Inc., London, 1974.
  • Strogatz, S.H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Addison-Wesley, Reading, MA, 1994.
  • Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos. No. 2 in Texts in Applied Mathematics. Springer-Verlag, New York, 1990.
Mechanics
  • Goldstein, H., Classical Mechanics. Addison-Wesley, Reading, MA, 2nd edn., 1980.
  • Lanczos, C., The Variational Principles of Mechanics, vol. 4 of Mathematical Expositions. University of Toronto Press, Toronto, 4th edn., 1970.