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Abstract
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Euler and Lagrange established a mathematically satisfactory foundation of Newtonian mechanics. Hamilton developed analogous formulation of optics. Jacobi imported Hamilton's idea in mechanics, and eventually arrived at a new formulation (now referred to as the Hamilton-Jacobi formalism).The Hamilton-Jacobi formalism was a crucial step towards Liouville'srigorous definition of the notion of ``integrability''. Moreover, Jacobi himself is also famous for having discovered (1839) that the geodesic motion on an ellipsoid is an integrablesystem (and solvable by hyperellipticfunctions) .
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