Motion of self-excited Froude pendulum under external forcing were analyzed. Differential equation of motion includes the nonlinear damping term of Rayleigh's type. Using multiple time scale method and Lyapunov theory, vibrations, synchronization and stability of the system were examined. Chaotic motion was analyzed here by means of Lyapunov exponent and Melnikov approach.
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Litak et al. (1999) studied this question.
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