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Reference.org
Castigliano's method
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<p>Castigliano's method, named after <a href="/facts/Carlo_Alberto_Castigliano/UzwTCC4b">Carlo Alberto Castigliano</a>, is a method for determining the displacements of a <a href="/facts/Linear_elasticity/pPLIvs7a">linear-elastic</a> system based on the <a href="/facts/Partial_derivative/JWHsBkAu">partial derivatives</a> of the <a href="/facts/Energy/wd8PrQM7">energy</a>. The basic concept may be easy to understand by recalling that a change in energy is equal to the causing force times the resulting displacement. Therefore, the causing force is equal to the change in energy divided by the resulting displacement. Alternatively, the resulting displacement is equal to the change in energy divided by the causing force. Partial derivatives are needed to relate causing forces and resulting displacements to the change in energy. </p>