Ingenieur-Archiv

, Volume 52, Issue 3–4, pp 167–176 | Cite as

Some aspects of Euler-Newton equations of motion

  • H. Hemami
Article

Summary

Euler-Newton's equations for a system of connected rigid bodies, written in a special state space form, provide a systematic method of arriving at the differential equations of the system. This method is amenable to programming and symbolic algebraic manipulation. The elimination of some or all forces of constraint is by projection, implementing the principle of virtual work, and is done by inner products. The computation of these forces requires symbolic inversion of a matrix for which an iterative scheme is proposed here. A method for construction of Lyapunov functions for stability of such systems in the vicinity of an arbitrary operating point is proposed. This construction may be achieved by symbolic manipulations and supplements applications of the Euler-Newton method.

Keywords

Lyapunov Function Operating Point Space Form Iterative Scheme Virtual Work 

Einige Aspekte der Euler-Newtonschen Bewegungsgleichungen

Übersicht

Euler-Newtonsche Gleichungen, dargestellt in einem besonderen Zustandsraum, liefern eine systematische Methode zur Herleitung der Differentialgleichungen eines Systems starr verbundener Körper. Diese Methode eignet sich für symbolisch algebraische Verfahren und zur Programmierung. Durch Projektion, unter Anwendung des Prinzips der virtuellen Arbeit und Berechnung der inneren Produkte, können einige oder alle Zwangskräfte eliminiert werden. Die Berechnung dieser Kräfte erfordert symbolische Matrixinversion, für die hier ein iteratives Verfahren vorgeschlagen wird. Ferner wird eine Methode vorgestellt, die zur Herleitung der Lyapunovschen Stabilitätsfunktion in der Umgebung eines beliebigen Arbeitspunktes dient. Die Lyapunovfunktion kann durch symbolische Verfahren und durch ergänzende Anwendungen der Euler-Newton Methode ermittelt werden.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • H. Hemami
    • 1
  1. 1.Department of Electrical EngineeringThe Ohio State UniversityColumbusUSA

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