This paper presents methods for determining the exact solutions of certain two-degree-of-freedom nonlinear systems with high-degree polynomial restoring forces. The exact solutions are the normal modes of the systems. A stability analysis of solutions in the normal modes is given. Some systems have normal modes whose stability is a function of amplitude. The stability of complicated systems can be approximated by superposing the stability characteristics of simpler systems. Some experimental confirmation by analog computer is also presented.
The Stability of the Normal Modes of Nonlinear Systems With Polynomial Restoring Forces of High Degree
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Atkinson, C. P., Bhatt, S. J., and Pacitti, T. (June 1, 1963). "The Stability of the Normal Modes of Nonlinear Systems With Polynomial Restoring Forces of High Degree." ASME. J. Appl. Mech. June 1963; 30(2): 193–198. https://doi.org/10.1115/1.3636511
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