In mathematical physics, **analytical mechanics** is a term used for a refined, mathematical form of classical mechanics, constructed from the 18th century onwards as a formulation of the subject as founded by Isaac Newton and Galileo Galilei. Often the term **vectorial mechanics** is applied to the form based on Newton's work, to contrast it with analytical mechanics which uses two *scalar* properties of motion, the kinetic and potential energies, instead of vector forces, to analyze the motion.

The subject has two principal parts: Lagrangian mechanics and Hamiltonian mechanics, both are tightly intertwined.

Analytical mechanics was primarily developed to extend the scope of classical mechanics in a systematic, generalized and efficient way to solve problems using the concept of *constraints* on systems and *paths integrals*. However, the concepts lead theoretical physicists, in particular SchrÃ¶dinger, Dirac, Heisenberg and Feynman, to the development of quantum mechanics, and its refinement - quantum field theory. Applications and extensions also reach into Einstein's general relativity, and chaos theory. A very general result from classical analytical mechanics is Noether's theorem, which fuels much of modern theoretical physics.

Read more about Analytical Mechanics: Intrinsic Motion, Lagrangian Mechanics, Hamiltonian Mechanics, Properties of The Lagrangian and Hamiltonian Functions, Hamiltonian-Jacobi Mechanics, Extensions To Classical Field Theory, Routhian Mechanics, Symmetry, Conservation, and Noether's Theorem

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—Sir Arthur Conan Doyle (1859–1930)

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—Simone Weil (1909–1943)