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Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes^[1][2][3] (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics.
It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light.
It can also be defined as a branch of science which deals with the motion of and forces on objects. The field is yet less widely understood in terms of quantum theory.

Classical versus quantum

Part of a series of articles about
Classical mechanics
F→=ma→{displaystyle {vec {F}}=m{vec {a}}} Second law of motion
History Timeline
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanics
Core topics Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity
Scientists Galileo Huygens Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy
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Part of a series on
Quantum mechanics
iℏ∂∂t|ψ(t)⟩=H^|ψ(t)⟩{displaystyle ihbar {frac {partial }{partial t}}|psi (t)rangle ={hat {H}}|psi (t)rangle } Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Coherence Decoherence Complementarity Energy level Entanglement Hamiltonian Uncertainty principle Ground state Interference Measurement Nonlocality Observable Operator Quantum Quantum fluctuation Quantum foam Quantum levitation Quantum number Quantum noise Quantum realm Quantum state Quantum system Quantum teleportation Qubit Spin Superposition Symmetry (Spontaneous) symmetry breaking Vacuum state Wave propagation Wave function Wave function collapse Wave–particle duality Matter wave
Effects Zeeman effect Stark effect Aharonov–Bohm effect Landau quantization Quantum Hall effect Quantum Zeno effect Quantum tunnelling Photoelectric effect Casimir effect
Experiments Afshar Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser (delayed-choice) Schrödinger's cat Quantum suicide and immortality Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path-integral) Hellmann–Feynman theorem
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Bayesian Quantum logic Relational Stochastic Scale relativity Transactional
Advanced topics Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory (quantum mechanics) Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics
Scientists Aharonov Bell Blackett Bloch Bohm Bohr Born Bose de Broglie Candlin Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger
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Historically, classical mechanics came first and quantum mechanics is a comparatively recent development. Classical mechanics originated with Isaac Newton's laws of motion in Philosophiæ Naturalis Principia Mathematica; Quantum Mechanics was developed in the early 20th century. Both 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 sciences. 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. 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 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 traveled 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 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 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 versus Newtonian

In analogy to the distinction between quantum and classical mechanics, Einstein's general and special theories of relativity have expanded the scope of Newton and Galileo's formulation of mechanics. The differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a massive body approaches the speed of light. For instance, in Newtonian mechanics, Newton's laws of motion specify that F = ma, whereas in relativistic mechanics and Lorentz transformations, which were first discovered by Hendrik Lorentz, F = γma (where γ is the Lorentz factor, which is almost equal to 1 for low speeds).

General relativistic versus quantum

Relativistic corrections are also needed for quantum mechanics, although general relativity has not been integrated. The two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything.

History

Antiquity

The main theory of mechanics in antiquity was Aristotelian mechanics.^[4] A later developer in this tradition is Hipparchus.^[5]

Medieval age

Arabic Machine Manuscript. Unknown date (at a guess: 16th to 19th centuries).

In the Middle Ages, Aristotle's theories were criticized and modified by a number of figures, beginning with John Philoponus in the 6th century. A central problem was that of projectile motion, which was discussed by Hipparchus and Philoponus. This led to the development of the theory of impetus by 14th-century French priest Jean Buridan, which developed into the modern theories of inertia, velocity, acceleration and momentum. This work and others was developed in 14th-century England by the Oxford Calculators such as Thomas Bradwardine, who studied and formulated various laws regarding falling bodies.

On the question of a body subject to a constant (uniform) force, the 12th-century Jewish-Arab Nathanel (Iraqi, of Baghdad) stated that constant force imparts constant acceleration, while the main properties 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 and Isaac Newton. Galileo's final statement of his mechanics, particularly of falling bodies, is his Two New Sciences (1638). Newton's 1687 Philosophiæ Naturalis Principia Mathematica provided a detailed mathematical account of mechanics, using the newly developed mathematics of calculus and providing the basis of Newtonian mechanics.^[5]

There is some dispute over priority of various ideas: Newton's Principia is certainly the seminal work and has been tremendously influential, and the systematic mathematics therein did not and could not have been stated earlier because calculus had not been developed. However, many of the ideas, particularly as pertain to inertia (impetus) and falling bodies had been developed and stated by earlier researchers, both the then-recent Galileo 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 of Einstein, and quantum mechanics, 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, projectiles, spacecraft, stars, parts of machinery, parts of solids, parts of fluids (gases and liquids), 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, such as orientation in space.

Otherwise, bodies may be semi-rigid, i.e. elastic, or non-rigid, i.e. fluid. These subjects have both classical and quantum divisions of study.

For instance, the motion of a spacecraft, regarding its orbit and attitude (rotation), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus 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. 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 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

Play media

Prof. Walter Lewin explains Newton's law of gravitation in MIT course 8.01^[6]

The following are described as forming classical mechanics:

• 
  Newtonian mechanics, the original theory of motion (kinematics) and forces (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, 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 thermodynamic properties.


• 
  Celestial mechanics, the motion of bodies in space: planets, comets, stars, galaxies, etc.


• 
  Astrodynamics, spacecraft navigation, etc.


• 
  Solid mechanics, elasticity, plasticity, 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, or Engineering mechanics


• 
  Biomechanics, solids, fluids, etc. in biology


• 
  Biophysics, physical processes in living organisms


• 
  Relativistic or Einsteinian mechanics, universal gravitation.

Quantum

The following are catgorized as being part of quantum mechanics:

• 
  Schrödinger wave mechanics, used to describe the movements of the wavefunction of a single particle.


• 
  Matrix mechanics is an alternative formulatio 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 thermodynamic properties.


• 
  Particle physics, the motion, structure, and reactions of particles


• 
  Nuclear physics, the motion, structure, and reactions of nuclei


• 
  Condensed matter physics, quantum gases, solids, liquids, etc.

Professional organizations

• 
  Applied Mechanics Division, American Society of Mechanical Engineers
  


• Fluid Dynamics Division, American Physical Society
  


• 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


• Dynamics


• Engineering


• Index of engineering science and mechanics articles


• Kinematics


• Kinetics


• Non-autonomous mechanics


• Statics


• Wiesen Test of Mechanical Aptitude (WTMA)

References

Further reading

• 
  Robert Stawell Ball (1871) Experimental Mechanics from Google books.


• 
  Landau, L. D.; Lifshitz, E. M. (1972). Mechanics and Electrodynamics, Vol. 1. Franklin Book Company, Inc. ISBN 978-0-08-016739-8.CS1 maint: Multiple names: authors list (link)
  

External links

Look up mechanics in Wiktionary, the free dictionary.

• iMechanica: the web of mechanics and mechanicians


• Mechanics Definition


• 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


• Engineering Fundamental Solid & Fluid Mechanics