Mechanical Systems: Equations of Motion and Stability

Abstract

The Chapter ‘Mechanical Systems: Equations of Motion and Stability’ corresponds to the material presented in five lectures given at the CISM Course no. 418. The first parts deal with the form of the equations of motion of mechanical systems, in particular the linearized equations and the influence and importance of the different terms (inertia terms, damping, gyroscopic terms, restoring terms and circulatory terms as well as with their physical origin). This is done both for discrete systems, and the corresponding material is part of the recent book Hagedorn & Hochlenert, Technische Schwingungslehre, Verlag Harri Deutsch, Frankfurt, 2012, as well as for continuous systems, the material being adapted from Hagedorn & DasGupta, Vibrations and Waves in Continuous Mechanical Systems, Wiley, Chichester, 2007. Almost all the material is presented in typical elementary vibration courses, but here certain aspects will be highlighted, which are not always stressed in basic vibration courses. The third part deals with Liapounov stability, the material is from the author’s earlier book Hagedorn, Non-Linear Oscillations, 2nd edition, Oxford Science Publications, 1988. The material of these five lectures is used in the other lectures of the course.The author prepared most of the material in 2012 and 2013, while staying at the University of Canterbury in Christchurch, New Zealand. The author thanks the Department of Mechanical Engineering of the UC for providing the infrastructure and assistance.KeywordsMechanical SystemTrivial SolutionNegative Real PartPositive Real PartFollower ForceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.