Answer
Variations: Poisson's contributions centered around the calculus of variations, a mathematical technique used to find extrema (minimum or maximum values) of functionals. Functionals are functions that take other functions as inputs, and the calculus of variations provides a systematic method for determining the functions that optimize these functionals. Poisson's work in this field laid the groundwork for advancements in celestial mechanics, elasticity, and other areas of physics and engineering.