Analytical Mechanics

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 Schrödinger, 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

Famous quotes containing the words analytical and/or mechanics:

    I have seen too much not to know that the impression of a woman may be more valuable than the conclusion of an analytical reasoner.
    Sir Arthur Conan Doyle (1859–1930)

    It is only the impossible that is possible for God. He has given over the possible to the mechanics of matter and the autonomy of his creatures.
    Simone Weil (1909–1943)