Definition:Euler-Lagrange Equation/Historical Note

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Historical Note on Euler-Lagrange Equation

The Euler-Lagrange equation was developed in the $1750$s by Leonhard Paul Euler and Joseph Louis Lagrange in connection with their studies of the Tautochrone Problem.

Lagrange solved it in $1755$ and sent the solution to Euler.

They further developed Lagrange's method and applied it to mechanics.

This led to the formulation of Lagrangian mechanics.

Their correspondence ultimately led to the calculus of variations.