Editing Mechanics (section)

== Sub-disciplines ==
The following are the three main designations consisting of various subjects that are studied in mechanics.

Note that there is also the "[[Field theory (physics)|theory of fields]]" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether it be [[Classical field theory|classical fields]] or [[quantum field theory|quantum fields]]. But in actual practice, subjects belonging to mechanics and fields are closely interwoven. Thus, for instance, forces that act on particles are frequently derived from fields ([[Electromagnetism|electromagnetic]] or [[gravitational]]), and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the [[wave function]].

=== Classical ===
{{main|Classical mechanics}}
[[File:Newtonslawofgravity.ogv|thumb|Prof. [[Walter Lewin]] explains [[Newton's law of universal gravitation|Newton's law of gravitation]] in [[MIT]] course 8.01<ref>
{{cite video
 | people      = [[Walter Lewin]]   | date        = October 4, 1999
 | title       = Work, Energy, and Universal Gravitation. MIT Course 8.01: Classical Mechanics, Lecture 11.
 | url         = http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-11/
 | format      = ogg   | medium      = videotape  | publisher   = [[MIT OpenCourseWare|MIT OCW]]   | location    = Cambridge, MA US 
 | access-date  = December 23, 2010  | time   = 1:21-10:10  | ref   = lewin
}}</ref> ]]
The following are described as forming classical mechanics:
* [[Newtonian mechanics]], the original theory of motion ([[kinematics]]) and forces ([[Analytical dynamics|dynamics]])
* [[Analytical mechanics]] is a reformulation of Newtonian mechanics with an emphasis on system energy, rather than on forces. There are two main branches of analytical mechanics:
** [[Hamiltonian mechanics]], a theoretical [[Formalism (mathematics)|formalism]], based on the principle of conservation of energy
** [[Lagrangian mechanics]], another theoretical formalism, based on the principle of the [[least action]]
* [[Classical statistical mechanics]] generalizes ordinary classical mechanics to consider systems in an unknown state; often used to derive [[thermodynamics|thermodynamic]] properties.
* [[Celestial mechanics]], the motion of bodies in space: planets, comets, stars, [[galaxies]], etc.
* [[Astrodynamics]], spacecraft [[navigation]], etc.
* [[Solid mechanics]], [[Elasticity (physics)|elasticity]], [[Plasticity (physics)|plasticity]], or [[viscoelasticity]] exhibited by deformable solids
* [[Fracture mechanics]] 
* [[Acoustics]], [[sound]] (density, variation, propagation) in solids, fluids and gases
* [[Statics]], semi-rigid bodies in [[mechanical equilibrium]]
* [[Fluid mechanics]], the motion of fluids
* [[Soil mechanics]], mechanical behavior of soils
* [[Continuum mechanics]], mechanics of continua (both solid and fluid)
* [[Hydraulics]], mechanical properties of liquids
* [[Fluid statics]], liquids in equilibrium
* [[Applied mechanics]] (also known as engineering mechanics)
* [[Biomechanics]], solids, fluids, etc. in biology
* [[Biophysics]], physical processes in living organisms
* [[Relativistic physics|Relativistic]] or [[Albert Einstein|Einsteinian]] mechanics

=== Quantum ===
{{main|Quantum mechanics}}
The following are categorized as being part of quantum mechanics:
* [[Schrödinger equation|Schrödinger wave mechanics]], used to describe the movements of the wavefunction of a single particle.
* [[Matrix mechanics]] is an alternative formulation that allows considering systems with a finite-dimensional state space.
* [[Quantum statistical mechanics]] generalizes ordinary quantum mechanics to consider systems in an unknown state; often used to derive [[thermodynamics|thermodynamic]] properties.
* [[Particle physics]], the motion, structure, and behavior of fundamental particles
* [[Nuclear physics]], the motion, structure, and reactions of nuclei
* [[Condensed matter physics]], quantum gases, solids, liquids, etc.

Historically, [[classical mechanics]] had been around for nearly a quarter millennium before quantum mechanics developed. Classical mechanics originated with [[Isaac Newton]]'s [[Newton's laws of motion|laws of motion]] in [[Philosophiæ Naturalis Principia Mathematica]], developed over the seventeenth century. Quantum mechanics developed later, over the nineteenth century, precipitated by [[Planck postulate|Planck's postulate]] and Albert Einstein's explanation of the [[photoelectric effect]]. Both fields are commonly held to constitute the most certain knowledge that exists about physical nature.

Classical mechanics has especially often been viewed as a model for other so-called [[exact science]]s. Essential in this respect is the extensive use of [[mathematics]] in theories, as well as the decisive role played by [[experiment]] in generating and testing them.

Quantum mechanics is of a bigger scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the [[correspondence principle]], there is no contradiction or conflict between the two subjects, each simply pertains to specific situations. The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large [[quantum numbers]], i.e. if quantum mechanics is applied to large systems (for e.g. a baseball), the result would almost be the same if classical mechanics had been applied. Quantum mechanics has superseded classical mechanics at the foundation level and is indispensable for the explanation and prediction of processes at the molecular, atomic, and sub-atomic level. However, for macroscopic processes classical mechanics is able to solve problems which are unmanageably difficult (mainly due to computational limits) in quantum mechanics and hence remains useful and well used.
Modern descriptions of such behavior begin with a careful definition of such quantities as displacement (distance moved), time, velocity, acceleration, mass, and force. Until about 400 years ago, however, motion was explained from a very different point of view. For example, following the ideas of Greek philosopher and scientist Aristotle, scientists reasoned that a cannonball falls down because its natural position is in the Earth; the Sun, the Moon, and the stars travel in circles around the Earth because it is the nature of heavenly objects to travel in perfect circles.

Often cited as father to modern science, [[Galileo]] brought together the ideas of other great thinkers of his time and began to calculate motion in terms of distance travelled from some starting position and the time that it took. He showed that the speed of falling objects increases steadily during the time of their fall. This acceleration is the same for heavy objects as for light ones, provided air friction (air resistance) is discounted. The English mathematician and physicist [[Isaac Newton]] improved this analysis by defining force and mass and relating these to acceleration. For objects traveling at speeds close to the speed of light, Newton's laws were superseded by [[Albert Einstein]]'s [[Special relativity|theory of relativity]]. [A sentence illustrating the computational complication of Einstein's theory of relativity.] For atomic and subatomic particles, Newton's laws were superseded by [[Quantum mechanics|quantum theory]]. For everyday phenomena, however, Newton's three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion.

=== Relativistic ===
{{main|Relativistic mechanics}}
Akin to the distinction between quantum and classical mechanics, [[Albert Einstein]]'s [[General relativity|general]] and [[Special relativity|special]] theories of [[theory of relativity|relativity]] have expanded the scope of [[Isaac Newton|Newton]] and [[Galileo]]'s formulation of mechanics. The differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a body approaches the [[speed of light]]. For instance, in [[classical mechanics|Newtonian mechanics]], the [[kinetic energy]] of a [[free particle]] is {{math|1=''E'' = {{sfrac|1|2}}''mv''<sup>2</sup>}}, whereas in relativistic mechanics, it is {{math|1=''E'' = (''γ'' − 1)''mc''<sup>2</sup>}} (where {{math|''γ''}} is the [[Lorentz factor]]; this formula reduces to the Newtonian expression in the low energy limit).<ref>{{cite book |last1=Landau |first1=L. |last2=Lifshitz |first2=E. |title=The Classical Theory of Fields |date=January 15, 1980 |publisher=Butterworth-Heinemann |page=27 |edition=4th Revised English}}</ref>

For high-energy processes, quantum mechanics must be adjusted to account for special relativity; this has led to the development of [[quantum field theory]].<ref>{{cite book |last1=Weinberg |first1=S. |title=The Quantum Theory of Fields, Volume 1: Foundations |date=May 1, 2005 |publisher=Cambridge University Press |isbn=0-521-67053-5 |page=xxi |edition=1st}}</ref>