Virtual work
Concept in mechanics linking virtual displacements to work.
Virtual work is a concept in mechanics that arises from the application of the principle of least action to the study of forces and movement of a mechanical system. It refers to the work of a force acting on a particle along a virtual displacement, which is one of the possible displacements that a particle may follow. Among all such virtual displacements, the one that minimizes the action is the actual displacement followed by the particle.
- field
- Mechanics
- known_for
- Principle of virtual work, virtual displacements, calculus of variations
- related_principles
- Principle of least action, D'Alembert's principle
Lore & Background
The principle of virtual work has been used in some form since antiquity in the study of statics, appearing as 'the law of lever' among the Greeks, medieval Arabs and Latins, and Renaissance Italians. In the 17th century, notable physicists such as Galileo, Descartes, Torricelli, Wallis, and Huygens invoked the idea of virtual work in varying degrees of generality when solving problems in statics. Johann Bernoulli systematized the virtual work principle and made explicit the concept of infinitesimal displacement, solving problems for both rigid bodies and fluids.
Reader's Guide
Virtual work is significant as a foundational concept in mechanics, historically formulated to analyze systems of rigid bodies and later developed for deformable bodies. Lagrange considered the virtual work principle more fundamental than the least action principle, as it could be assumed alone as the foundation for all mechanics, unlike the least action principle which does not account for non-conservative forces. The formal procedure for computing the difference of functions evaluated on nearby paths is the calculus of variations.
Did You Know?
- The principle of virtual work was used in antiquity as 'the law of lever' by the Greeks, medieval Arabs and Latins, and Renaissance Italians.
- Lagrange considered the virtual work principle more fundamental than the least action principle because it could be assumed alone as the foundation for all mechanics.
More in Classical And Continuum Mechanics 1-19
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