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The Lazy UniverseAn Introduction to the Principle of Least Action$
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Jennifer Coopersmith

Print publication date: 2017

Print ISBN-13: 9780198743040

Published to Oxford Scholarship Online: June 2017

DOI: 10.1093/oso/9780198743040.001.0001

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The Principle of Virtual Work

The Principle of Virtual Work

(p.59) 4 The Principle of Virtual Work
The Lazy Universe

Jennifer Coopersmith

Oxford University Press

The meaning behind the mysterious Principle of Virtual Work is explained. Some worked examples in statics (equilibrium) are given, and the method of Virtual Work is compared and contrasted with the method of Newtonian Mechanics. The meaning of virtual displacements is explained very carefully. They must be ‘small’, happen simultaneously, and do not cause a force, result froma force, or take any time to occur. Counter to intuition, not all the actual displacements can be allowed as virtual displacements. Some examples worked through are: Feynman’s pivoting (cantilever) bar, a “black box,” a weighted spring, a ladder, a capacitor, a soap bubble, and Atwood’s machine. The links between mechanics and geometry are demonstrated, and it is shown how the reaction or constraint forces are always perpendicular to the virtual displacements. Lanczos’s Postulate A and its astounding universality are explained.

Keywords:   Virtual Work, statics, equilibrium, cantilever, black box, weighted spring, soap bubble, Atwood’s machine, reaction force, constraints

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