Non-Local Methods for Pendulum-Like Feedback Systems

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0 are already deecribed by I. Newton (116]. However it was 250 years later that F. Tricorni (147] carried out the first non-local qualitative investigation of equation (0.1) with arbitrary o 0 and ‘{ 0. It was proved by F. Tricorni that any solution of (0.1) with o > 0 corresponds either to a rotatory motion or to a damped oscillatory motion. Moreover, he showed that in the non-trivial case ’!::: 1 there exists a bifurcation value ocr( ‘!) corresponding to a separatrix-loop, i.e. to a double-asymptotic to a saddle-point trajectory. For o ocr( “) global asymptotic stability takes place, i.e. every motion is a damped oscillation. The papers of F. Tricorni became familiar immediately.