Integral Variational Formulations

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


D’Alembert’s principle and Gauss’ principle of least constraint are examples of differential variational formulations. These formulations make independent statements at each instant of time during the motion. By contrast integral variational formulations, which we shall examine in this chapter, make a single, all inclusive, statement. That is, the motion over an arbitrary period of time is considered as a whole. While the various differential and integral variational formulation take different forms, they are of course related and they make equivalent statements about the motion.


Configuration Space Virtual Work Constraint Force Nonholonomic Constraint Generalize Displacement 
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Suggested Reading

  1. 1.
    Park, David,“Classical Dynamics and Its Quantum Analogues”, Second Edition, Springer-Verlag, (1989).Google Scholar
  2. 2.
    Rosenberg, Reinhardt M.,“Analytical Dynamics of Discrete Systems”, Plenum Press, (1977)..Google Scholar
  3. 3.
    Lanczos, Cornelius,“The Variational Principles of Mechanics”, 4th Edition, Dover Publications Inc., (1986).Google Scholar
  4. 4.
    Goldstein, Herbert,“Classical Mechanics”,Second Edition, Addison-Wesley Publishing Company, (1980).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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