Classical Mechanics

Classical mechanics is a model of the physics of forces acting upon bodies. It is often referred to as “Newtonian mechanics” after Isaac Newton and his laws of motion. Mechanics is subdivided into statics, which models objects at rest, kinematics, which models objects in motion, and dynamics, which models objects subjected to forces. The classical mechanics of continuous and deformable objects iscontinuum mechanics, which can itself be broken down into solid mechanics and fluid mechanics according to the state of matter being studied. The latter, the mechanics of liquids and gases, includes hydrostaticshydrodynamicspneumaticsaerodynamics, and other fields.

An important concept of mechanics is the identification of conserved energy and momentum, which leads to the Lagrangian andHamiltonian reformulations of Newton’s laws. Liouville’s theorem for statistical and Hamiltonian mechanics is a classical 19th century result which describes the behavior of the phase space distribution function. Liouville’s theorem has a suggestive formulation, the Poisson bracket, which encodes Hamilton’s equations of classical mechanics, and has analogies with the commutator in quantum mechanics.

A relatively recent result of considerations concerning the dynamics of nonlinear systems is chaos theory, the study of systems in which small changes in a variable may have large effects.

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