Expositio paper exp-20260809-4d0c94
Calculus of Variations: An Introduction to the Optimization of Functionals
This paper describes the mathematical technique of calculus of variations starting with the derivation of key equations such as the Euler-Lagrange equation and the Beltrami Identity. These equations are then applied in the following scenarios: geodesic on a f…
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Abstract
This paper describes the mathematical technique of calculus of variations starting with the derivation of key equations such as the Euler-Lagrange equation and the Beltrami Identity. These equations are then applied in the following scenarios: geodesic on a flat plane, solving the Brachistochrone problem, geodesic on a sphere, and finding the equation of the function formed by a string under the influence of gravity(catenary problem).
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