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Mechanics (from
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek Dark ...
: μηχανική, ''mēkhanikḗ'', "of
machines A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engine An engine or motor is a machine designed to conve ...

machines
") is the area of
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

mathematics
and
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...

physics
concerned with the relationships between
force In physics, a force is an influence that can change the motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to accelerate. Force can ...

force
,
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
, and
motion In physics, motion is the phenomenon in which an object changes its Position (geometry), position with respect to time. Motion is mathematically described in terms of Displacement (geometry), displacement, distance, velocity, acceleration, speed ...

motion
among physical objects.
Force In physics, a force is an influence that can change the motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to accelerate. Force can ...

Force
s applied to objects result in displacements, or changes of an object's position relative to its environment. Theoretical expositions of this branch of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...

physics
has its origins in
Ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), th ...
, for instance, in the writings of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...

Aristotle
and
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, ...

Archimedes
(see
History of classical mechanics This article deals with the history of classical mechanics. Precursors to classical mechanics Antiquity The ancient Greek philosophy, Greek philosophers, Aristotle in particular, were among the first to propose that abstract principles go ...
and
Timeline of classical mechanics The following is a timeline of classical mechanics: Early mechanics * 4th century BC - Aristotle invents the system of Aristotelian physics, which is later largely disproved * 4th century BC - Babylonian astronomy, Babylonian astronomers calcula ...
). During the early modern period, scientists such as
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

Galileo
,
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe ...

Kepler
,
Huygens
Huygens
, and
Newton
Newton
laid the foundation for what is now known as
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of macroscopic objects, from projectiles to parts of Machine (mechanical), machinery, and astronomical objects, such as spacecraft, planets, stars, and galax ...
. As a branch of
classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm.


History


Antiquity

The ancient Greek philosophers were among the first to propose that abstract principles govern nature. The main theory of mechanics in antiquity was
Aristotelian mechanics Aristotelian physics is the form of Natural sciences, natural science described in the works of the Ancient Greek philosophy, Greek philosopher Aristotle (384–322 BC). In his work ''Physics (Aristotle), Physics'', Aristotle intended to establis ...
, though an alternative theory is exposed in the pseudo-Aristotelian '' Mechanical Problems'', often attributed to one of his successors. There is another tradition that goes back to the ancient Greeks where mathematics is used more extensively to analyze bodies
statically
statically
or dynamically, an approach that may have been stimulated by prior work of the Pythagorean
Archytas Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greece, Ancient Greek philosopher, mathematician, music theorist, astronomer, wikt:statesman, statesman, and military strategy, strategist. He was a scientist of the Pythagor ...

Archytas
. Examples of this tradition include pseudo-
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

Euclid
(''On the Balance''),
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, ...

Archimedes
(''On the Equilibrium of Planes'', ''On Floating Bodies''),
Hero A hero (feminine: heroine) is a real person or a main fictional character who, in the face of danger, combats adversity through feats of ingenuity, courage, or Physical strength, strength. Like other formerly gender-specific terms (like ...

Hero
(''Mechanica''), and Pappus (''Collection'', Book VIII).A Tiny Taste of the History of Mechanics
. The University of Texas at Austin.


Medieval age

In the Middle Ages, Aristotle's theories were criticized and modified by a number of figures, beginning with
John Philoponus John Philoponus (Greek language, Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, commentaries on Aristotle, Aristotelian commentator, Christian theology, Christian theologi ...
in the 6th century. A central problem was that of
projectile motion Projectile motion is a form of motion (physics), motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's planetary surface, surface, and moves along a curved path under the ac ...

projectile motion
, which was discussed by
Hipparchus Hipparchus (; el, wikt:Ἵππαρχος, Ἵππαρχος, ''Hipparkhos'';  BC) was a Ancient astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidenta ...
and Philoponus. Persian Islamic polymath
Ibn Sīnā Ibn Sina ( fa, ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (), was a Persians, Persian polymath who is regarded as one of the most significant physicians, astronomers, philosophers, and writers of the ...
published his theory of motion in ''
The Book of Healing ''The Book of Healing'' (; ; also known as ) is a Islamic science, scientific and Early Islamic philosophy, philosophical encyclopedia written by Avicenna, Abu Ali ibn Sīna (aka Avicenna) from medieval Persia, near Bukhara in Maverounnahr. He ...
'' (1020). He said that an impetus is imparted to a projectile by the thrower, and viewed it as persistent, requiring external forces such as
air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
to dissipate it. Ibn Sina made distinction between 'force' and 'inclination' (called "mayl"), and argued that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent. He also claimed that a projectile in a vacuum would not stop unless it is acted upon, consistent with Newton's first law of motion. On the question of a body subject to a constant (uniform) force, the 12th-century Jewish-Arab scholar Hibat Allah Abu'l-Barakat al-Baghdaadi (born Nathanel, Iraqi, of Baghdad) stated that constant force imparts constant acceleration. According to
Shlomo Pines Shlomo Pines (; ; August 5, 1908 in Charenton-le-Pont – January 9, 1990 in Jerusalem) was an Israeli scholar of Jewish philosophy, Jewish and Islamic philosophy, Islamic philosophy, best known for his English translation of Maimonides' ''Guide o ...
, al-Baghdaadi's theory of
motion In physics, motion is the phenomenon in which an object changes its Position (geometry), position with respect to time. Motion is mathematically described in terms of Displacement (geometry), displacement, distance, velocity, acceleration, speed ...
was "the oldest negation of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...

Aristotle
's fundamental dynamic law amely, that a constant force produces a uniform motion nd is thus ananticipation in a vague fashion of the fundamental law of
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of macroscopic objects, from projectiles to parts of Machine (mechanical), machinery, and astronomical objects, such as spacecraft, planets, stars, and galax ...
amely, that a force applied continuously produces acceleration" Influenced by earlier writers such as Ibn SinaSayili, Aydin. "Ibn Sina and Buridan on the Motion the Projectile". Annals of the New York Academy of Sciences vol. 500(1). p.477-482. and al-Baghdaadi, the 14th-century French priest
Jean Buridan Jean Buridan (; Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around prese ...
developed the
theory of impetus The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus John Philoponus (Greek language, Greek: ; ; c. 490 – ...

theory of impetus
, which later developed into the modern theories of
inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his Newton%27s_ ...

inertia
,
velocity Velocity is the directional derivative, directional speed of an physical object, object in motion as an indication of its time derivative, rate of change in position (vector), position as observed from a particular frame of reference and as m ...

velocity
,
acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Accelerations are Euclidean vector, vector quantities (in that they have Magnitude (mathematics), magnitude and Direction ...

acceleration
and
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...

momentum
. This work and others was developed in 14th-century England by the Oxford Calculators such as
Thomas Bradwardine Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric Clergy are formal leaders within established religions. Their roles and functions vary in different religious traditions, but usually involve presiding over specif ...
, who studied and formulated various laws regarding falling bodies. The concept that the main properties of a body are uniformly accelerated motion (as of falling bodies) was worked out by the 14th-century Oxford Calculators.


Early modern age

Two central figures in the early modern age are
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

Galileo Galilei
and
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

Isaac Newton
. Galileo's final statement of his mechanics, particularly of falling bodies, is his ''
Two New Sciences The ''Discourses and Mathematical Demonstrations Relating to Two New Sciences'' ( it, Discorsi e dimostrazioni matematiche intorno a due nuove scienze ) published in 1638 was Galileo Galilei's final book and a scientific testament covering muc ...
'' (1638). Newton's 1687 ''
Philosophiæ Naturalis Principia Mathematica (English language, English: ''Mathematical Principles of Natural Philosophy'') often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his Newton's law of universal gravitation, law of universa ...
'' provided a detailed mathematical account of mechanics, using the newly developed mathematics of
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

calculus
and providing the basis of
Newtonian mechanics Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
. There is some dispute over priority of various ideas: Newton's ''Principia'' is certainly the seminal work and has been tremendously influential, and many of the mathematics results therein could not have been stated earlier without the development of the calculus. However, many of the ideas, particularly as pertain to inertia and falling bodies, had been developed by prior scholars such as
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typica ...

Christiaan Huygens
and the less-known medieval predecessors. Precise credit is at times difficult or contentious because scientific language and standards of proof changed, so whether medieval statements are ''equivalent'' to modern statements or ''sufficient'' proof, or instead ''similar'' to modern statements and ''hypotheses'' is often debatable.


Modern age

Two main modern developments in mechanics are
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
of
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...

Einstein
, and
quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
, both developed in the 20th century based in part on earlier 19th-century ideas. The development in the modern continuum mechanics, particularly in the areas of elasticity, plasticity, fluid dynamics, electrodynamics and thermodynamics of deformable media, started in the second half of the 20th century.


Types of mechanical bodies

The often-used term body needs to stand for a wide assortment of objects, including
particles In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...

particles
,
projectiles A projectile is an object that is propelled by the application of an external force and then moves freely under the influence of gravity and air resistance. Although any objects in motion (physics), motion through space are projectiles, they are ...
,
spacecraft A spacecraft is a vehicle or machine designed to spaceflight, fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth ...

spacecraft
,
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

star
s, parts of
machinery A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...

machinery
, parts of
solids Solid is one of the four fundamental states of matter In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and Plasma (physics ...

solids
, parts of
fluids In physics, a fluid is a liquid, gas, or other material that continuously Deformation (physics), deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances wh ...

fluids
(
gases Gas is one of the four fundamental state of matter, states of matter (the others being solid, liquid, and plasma (physics), plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), chemical element, elemental molec ...
and
liquids A liquid is a nearly Compressibility, incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of State of matter#Four fundamental states, the four fund ...
), etc. Other distinctions between the various sub-disciplines of mechanics, concern the nature of the bodies being described. Particles are bodies with little (known) internal structure, treated as mathematical points in classical mechanics. Rigid bodies have size and shape, but retain a simplicity close to that of the particle, adding just a few so-called
degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variable Dependent and independent variables are variables in mathematical modeling, statistical model A statistical model is a mathematical model that emb ...
, such as orientation in space. Otherwise, bodies may be semi-rigid, i.e. elastic, or non-rigid, i.e.
fluid In physics, a fluid is a liquid, gas, or other material that continuously Deformation (physics), deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances wh ...
. These subjects have both classical and quantum divisions of study. For instance, the motion of a spacecraft, regarding its
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or pos ...
and attitude (
rotation Rotation, or spin, is the circular movement of an object around a ''axis of rotation, central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A t ...
), is described by the relativistic theory of classical mechanics, while the analogous movements of an
atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden experiments, Geiger–Marsden gold foil experiment. After th ...
are described by quantum mechanics.


Sub-disciplines

The following are two lists of various subjects that are studied in mechanics. Note that there is also the " theory of fields" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether classical fields or
quantum fields In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
. 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 (
electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
or
gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
), and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex number, complex-valued probability amplitude, and the probabilities for the possible results of ...
.


Classical

The following are described as forming classical mechanics: *
Newtonian mechanics Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
, the original theory of motion (
kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...
) and forces ( dynamics). *
Analytical mechanics In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the ...
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 Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
, a theoretical
formalism Formalism may refer to: * Form (disambiguation) * Formal (disambiguation) * Legal formalism, legal positivist view that the substantive justice of a law is a question for the legislature rather than the judiciary * Formalism (linguistics) * Scient ...
, based on the principle of conservation of energy. **
Lagrangian mechanics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Loui ...
, another theoretical formalism, based on the principle of the
least action The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the ''action (physics), action'' of a mechanics, mechanical system, yields the equations of motion for that syste ...
. * Classical statistical mechanics generalizes ordinary classical mechanics to consider systems in an unknown state; often used to derive
thermodynamic Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
properties. *
Celestial mechanics Celestial mechanics is the branch of astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronol ...
, the motion of bodies in space: planets, comets, stars,
galaxies A galaxy is a system of stars, stellar remnants, interstellar medium, interstellar gas, cosmic dust, dust, dark matter, bound together by gravity. The word is derived from the Ancient Greek, Greek ' (), literally 'milky', a reference to the ...
, etc. *
Astrodynamics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
, spacecraft
navigation Navigation is a field of study that focuses on the process of monitoring and controlling the motion, movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navi ...
, etc. *
Solid mechanics Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature chang ...
, elasticity, plasticity,
viscoelasticity In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both Viscosity, viscous and Elasticity (physics), elastic characteristics when undergoing deformation (engineering), deformation. Viscous mate ...
exhibited by deformable solids. *
Fracture mechanics Fracture mechanics is the field of mechanics Mechanics (from Ancient Greek: wikt:μηχανική#Ancient_Greek, μηχανική, ''mēkhanikḗ'', "of machine, machines") is the area of mathematics and physics concerned with the relati ...
*
Acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
,
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
( = density variation propagation) in solids, fluids and gases. *
Statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in mechanical equilibrium, st ...
, semi-rigid bodies in
mechanical equilibrium In classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of macroscopic objects, from projectiles to parts of Machine (mechanical), machinery, and astronomical objects, such as spacecraft, ...
*
Fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical engineering, mechanic ...
, the motion of fluids *
Soil mechanics Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and wat ...
, mechanical behavior of soils *
Continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as point particle, discrete particles. The French mathematician Augustin-Louis Cauchy was the first to fo ...
, mechanics of continua (both solid and fluid) *
Hydraulics Hydraulics (from Greek language, Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is th ...
, mechanical properties of liquids *
Fluid statics Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body " fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an i ...
, liquids in equilibrium * Applied mechanics, or Engineering mechanics *
Biomechanics Biomechanics is the study of the structure, function and motion of the mechanical aspects of biological systems, at any level from whole organisms to Organ (anatomy), organs, Cell (biology), cells and cell organelles, using the methods of mechani ...
, solids, fluids, etc. in biology *
Biophysics Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study Biology, biological phenomena. Biophysics covers all scales of biological organization, from Molecule, molecular to organismic ...
, physical processes in living organisms * Relativistic or Einsteinian mechanics, universal
gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
.


Quantum

The following are categorized as being part of
quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
: * Schrödinger wave mechanics, used to describe the movements of the wavefunction of a single particle. *
Matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of Atomic el ...
is an alternative formulation that allows considering systems with a finite-dimensional state space. *
Quantum statistical mechanics Quantum statistical mechanics is statistical mechanics applied to quantum mechanics, quantum mechanical systems. In quantum mechanics a statistical ensemble (mathematical physics), statistical ensemble (probability distribution over possible quantu ...
generalizes ordinary quantum mechanics to consider systems in an unknown state; often used to derive
thermodynamic Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
properties. *
Particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standa ...
, the motion, structure, and reactions of particles *
Nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
, the motion, structure, and reactions of nuclei *
Condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases which arise from electromagnetic forces between atoms. More ge ...
, quantum gases, solids, liquids, etc. Historically,
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of macroscopic objects, from projectiles to parts of Machine (mechanical), machinery, and astronomical objects, such as spacecraft, planets, stars, and galax ...
had been around for nearly a quarter millennium before
quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
developed. Classical mechanics originated with
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

Isaac Newton
's laws of motion in
Philosophiæ Naturalis Principia Mathematica (English language, English: ''Mathematical Principles of Natural Philosophy'') often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his Newton's law of universal gravitation, law of universa ...
, developed over the seventeenth century. Quantum mechanics developed later, over the nineteenth century, precipitated by Planck's postulate and Albert Einstein's explanation of the
photoelectric effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and Solid-stat ...
. 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 The exact sciences, sometimes called the exact mathematical sciences, are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences. Examples of the exact sciences are mathematics, optics O ...
s. Essential in this respect is the extensive use of
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

mathematics
in theories, as well as the decisive role played by
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs wh ...
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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science ...
, 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 Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

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 Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
. sentence illustrating the computational complication of Einstein's theory of relativity.For atomic and subatomic particles, Newton's laws were superseded by 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

In analogy to the distinction between quantum and classical mechanics,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
's
general A general officer is an Officer (armed forces), officer of highest military ranks, high rank in the army, armies, and in some nations' air forces, space forces, and marines or naval infantry. In some usages the term "general officer" refers t ...
and special theories of relativity have expanded the scope of and
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

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 The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
. For instance, in
Newtonian mechanics Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
, the
kinetic energy In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical sci ...
of a
free particle In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a "field-free" space. I ...
is , whereas in
relativistic mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science ...
, it is (where is the
Lorentz factor The Lorentz factor or Lorentz term is a quantity (physics), quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations ...
; this formula reduces to the Newtonian expression in the low energy limit). For high-energy processes, quantum mechanics must be adjusted to account for special relativity; this has led to the development of
quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, natural phenomena. This is in c ...
.


Professional organizations

* Applied Mechanics Division,
American Society of Mechanical Engineers The American Society of Mechanical Engineers (ASME) is an American professional association that, in its own words, "promotes the art, science, and practice of multidisciplinary engineering and allied sciences around the globe" via "continuing ...
*Fluid Dynamics Division,
American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...
* Society for Experimental Mechanics
Institution of Mechanical Engineers
is the United Kingdom's qualifying body for mechanical engineers and has been the home of Mechanical Engineers for over 150 years.
International Union of Theoretical and Applied Mechanics


See also

*
Applied mechanics Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and e ...
* Dynamics *
Engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
* Index of engineering science and mechanics articles *
Kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...
* Kinetics * Non-autonomous mechanics *
Statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in mechanical equilibrium, st ...
* Wiesen Test of Mechanical Aptitude (WTMA)


References


Further reading

* Robert Stawell Ball (1871
Experimental Mechanics
from
Google books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google, Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using o ...
. *


External links


iMechanica: the web of mechanics and mechanicians



Mechanics Blog by a Purdue University Professor

The Mechanics program at Virginia Tech

Physclips: Mechanics with animations and video clips
from the University of New South Wales
U.S. National Committee on Theoretical and Applied Mechanics

Interactive learning resources for teaching Mechanics

The Archimedes Project
{{Authority control Articles containing video clips