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Differential Variational Formulations

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

Abstract

D’Alembert brought the problems of motion under the umbrella of problems of equilibrium. Using Euler’s linear momentum law (1.1.2), we have that, when a point mass is acted upon by a set of forces resulting in F, it will acquire a linear momentum B, such that
$$F = \dot B$$
(2.1.1)
Consider now an increment of work done by the force F, as well as by D’Alembert’s inertial force \( - \dot B\), as the point mass undergoes an imagined virtual displacement δr. Then
$$\delta {W_1} = \left( {F - \dot B} \right)\cdot \delta r = 0$$
(2.1.2)
because of relation (2.1.1).

Keywords

Inertial Force Configuration Space Virtual Work Potential Energy Function Virtual Displacement 
These 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.

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Suggested Reading

  1. 1.
    Crandall, Stephen H., Karnopp, Dean C., Kurtz, David F. Jr., PridmoreBrown, David C., “Dynamics of Mechanical and Electromechanical Systems”, McGraw-Hill, (1968).Google Scholar
  2. 2.
    Greenwood, Donald T., “Classical Dynamics”, Prentice-Hall, (1977).Google Scholar
  3. 3.
    Wells, Dare A., “Lagrangian Dynamics”, Schaum Publishing Co. (1967).Google Scholar
  4. 4.
    Lanczos Cornelius, “The Variational Principles of Mechanics”, Dover Publications Inc. 4th edition (1986).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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