Format:
1 Online-Ressource (VII, 242 S.)
ISBN:
9783663122616
,
9783663122623
Series Statement:
TEUBNER-TEXTE zur Mathematik
Note:
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("'!) equation (0.1) admits damped oscillations as weil as rotatory motions. For o 〉 ocr("'') global asymptotic stability takes place, i.e. every motion is a damped oscillation. The papers of F. Tricorni became familiar immediately
Language:
German
Keywords:
Regelungssystem
;
Pendelgleichung
;
Stabilität
;
Verzweigung
;
Ljapunov-Funktion
;
Differentialgleichungssystem
;
Zylinderbereich
;
Phasenraum
DOI:
10.1007/978-3-663-12261-6
