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Dynamic and Static Stability

  • Lester W. Schmerr
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 254)

Abstract

The motion of dynamical systems is strongly dependent on whether their behavior is stable or unstable. This chapter obtains the conditions which determine stability for certain types of systems that we have analyzed in previous chapters, using a direct method that involves the properties of the potential energy or the dynamic potential energy. We also discuss an indirect method that first requires the linearization of the equations of motion, but which is applicable to a wider class of systems. Since the direct dynamic stability method relies on the behavior of the potential energy, a quantity that in most dynamical systems is independent of time, this stability criterion is also applicable to static systems, i.e., systems that are designed to inherently be in equilibrium. Stability of static systems is rarely treated in any depth in traditional statics or dynamics courses so we will also analyze some of the important ways in which such static systems can lose stability.

References

  1. 1.
    R.M. Rosenberg, Analytical Dynamics of Discrete Systems (Plenum Press, New York, 1977)CrossRefGoogle Scholar
  2. 2.
    M.R.M. Crespo Da Silva, Fundamentals of Dynamics and Analysis of Motion (Dover Publications, New York, 2016)Google Scholar
  3. 3.
    H.L. Langhaar, Energy Methods in Applied Mechanics (John Wiley, New York, 1962)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lester W. Schmerr
    • 1
  1. 1.Aerospace EngineeringIowa State UniversityAmesUSA

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