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The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes.
Analytical mechanics aims at even more: not at understanding the mathematical structure of a single mechanical problem, but that of a class of problems so wide that they encompass most of mechanics. It concentrates on systems to which Lagrangian or Hamiltonian equations of motion are applicable and that include a very wide range of problems indeed.