Theorie Und Anwendung Der Direkten Methode Von Ljapunov
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Die grundlegende Arbeit von A. M. LJAPUNOV (1857 bis 1918) über die Stabilität der Bewegung, die 1892 in russischer Sprache, 1907 in französischer Übersetzung! erschien, hat ursprünglich nur wenig Beach- tung gefunden und war lange Zeit hindurch nahezu vergessen. Erst vor etwa 25 Jahren wurden diese Untersuchungen von einigen sowjetischen Mathematikern wieder aufgegriffen. Man bemerkte dabei, da sich die Ljapunovschen Ansätze zur Bewältigung konkreter Probleme der Physik und Technik eigneten, und seitdem befa t man sich, wie die wachsende Zahl der Veröffentlichungen erkennen lä t, in steigendem Ma e mit der von LJAPUNOV begründeten Stabilitätstheorie. Vor allem gilt das für die sogenannte zweite oder direkte Methode. LJAPUNOV hat sie eigentlich nur zur Ableitung von Stabilitätskriterien der theoretischen Mechanik benutzt. Jetzt verwendet man sie einerseits bei praktischen Aufgaben aus dem Bereich der mechanischen und elektrischen Schwin- gungen, insbesondere in der Regelungstechnik; andererseits hat man erkannt, da die direkte Methode als leitendes Prinzip einer allgemeinen Stabilitätstheorie dienen kann, die erheblich mehr umfa t als die bei gewöhnlichen Differentialgleichungen auftretenden Probleme. Die Theorie der direkten Methode ist in den letzten Jahren sehr gefördert und zu einem gewissen Abschlu gebracht worden. Sie kann daher jetzt in einem zusammenfassenden Ergebnisbericht dargestellt werden. Eine Übersicht, die diese Dinge einem grö eren Kreise näher- bringen kann, erscheint um so mehr angezeigt, als fast die gesamte Literatur in russischer Sprache und an teilweise schwer zugänglichen Stellen erschienen isP.
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