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.