The Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations. The Euler–Lagrange equation serves to extremize action functionals of the form I [ u ] = ∫ a b L [ x , u ( x ) , u ′ ( x ) ] d x , {\displaystyle I[u]=\int _{a}^{b}L[x,u(x),u'(x)]\,dx\,,} where a {\displaystyle a} and b {\displaystyle b} are constants and u ′ ( x ) = d u d x {\displaystyle u'(x)={\frac {du}{dx}}} .
The Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations. The Euler–Lagrange equation serves to extremize action functionals of the form I [ u ] = ∫ a b L [ x , u ( x ) , u ′ ( x ) ] d x , {\displaystyle I[u]=\int _{a}^{b}L[x,u(x),u'(x)]\,dx\,,} where a {\displaystyle a} and b {\displaystyle b} are constants and u ′ ( x ) = d u d x {\displaystyle u'(x)={\frac {du}{dx}}} .
Source: Wikipedia "Beltrami identity" · CC BY-SA 4.0
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