The principle of virtual velocities

  • Danilo Capecchi
Part of the Science Networks. Historical Studies book series (SNHS, volume 42)


This chapter is almost entirely devoted to Johann Bernoulli, who considers the equilibrium for a set of infinitesimal displacements and forces. In the first part the different conceptions of the force of the XVIII century, including those of dead and living forces, are summarized. In the central part Bernoulli’s VWL is presented which enforces equality of positive and negative energies, the energy being defined as the scalar product of the force by the displacement of its application point, named virtual velocity. He offers a number of applications to the various cases including the fluid but does not provide any demonstration. In the final part a comparison of Varignon’s mechanics, based on composition of forces and Bernoulli’s mechanics based on his VWL is considered.


Static Moment Incline Plane Incipient Motion Dead Force Absolute Force 
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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Danilo Capecchi
    • 1
  1. 1.Università La SapienzaRomeItaly

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