Special Applications

  • B. Tabarrok
  • F. P. J. Rimrott
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 31)


The Lagrangian equations of motion often take the form of second-order nonlinear differential equations. Such equations rarely admit analytical solutions. In some cases it is possible to linearize the equations of motion by imposition of some acceptable approximations. The linearized equations may then be solved analytically. An important class of such problems is the case of small amplitude oscillations about a position of equilibrium or about a predetermined steady motion. The process of linearization may be carried out on the differential equations or one may introduce the pertinent approximations when the energy and virtual work terms are written down. In this chapter we outline the latter procedure and describe methods of solution for the linearized equations.


Virtual Work Steady Motion Small Amplitude Oscillation Virtual Velocity Undamped System 
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Suggested Reading

  1. 1.
    Rao, Singiresu S. “Mechanical Vibrations” Addison-Wesley, (1990).Google Scholar
  2. 2.
    Thomson, William, T., “Theory of Vibrations with Applications”, 3rd Edition, Prentice-Hall, (1988).Google Scholar
  3. 3.
    Easthope, C.E., “Three Dimensional Dynamics — A Vectorial Treatment” Butterwoths, (1964).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • B. Tabarrok
    • 1
  • F. P. J. Rimrott
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of VictoriaVictoriaCanada
  2. 2.Department of Mechanical EngineeringUniversity of TorontoTorontoCanada

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