The Info List - Mechanics

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(Greek μηχανική) is that area of science which is 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
Ancient Greece
with the writings of Aristotle
and Archimedes[1][2][3] (see History of classical mechanics
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.


1 Classical versus quantum 2 Relativistic versus Newtonian 3 General relativistic versus quantum 4 History

4.1 Antiquity 4.2 Medieval age 4.3 Early modern age 4.4 Modern age

5 Types of mechanical bodies 6 Sub - disciplines

6.1 Classical 6.2 Quantum

7 Professional organizations 8 See also 9 References 10 Further reading 11 External links

Classical versus quantum[edit]

Part of a series of articles about

Classical mechanics

F →

= m

a →

displaystyle vec F =m vec a

Second law of motion

History Timeline


Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical


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


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


Circular motion Rotating reference frame Centripetal force Centrifugal force


Coriolis force Pendulum Tangential speed Rotational speed

Angular acceleration / displacement / frequency / velocity


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 of articles about

Quantum mechanics

i ℏ

∂ 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


Classical mechanics Old quantum theory Bra–ket notation

Hamiltonian Interference


Casimir effect Complementarity Hamiltonian Operator Quantum coherence Quantum decoherence Energy
level Ground state Vacuum state Zero-point energy QED vacuum QCD vacuum Measurement Quantum Quantum realm Quantum annealing Quantum entanglement Quantum superposition Quantum nonlocality Quantum system Quantum state Quantum number Quantum noise Quantum fluctuation Quantum foam Heisenberg uncertainty principle Photon entanglement Spontaneous parametric down-conversion Spin Scattering theory Symmetry Symmetry breaking Spontaneous symmetry breaking Quantum tunnelling Quantum levitation Quantum teleportation Wave
propagation Quantum interference Wave

Wave function
Wave function
collapse Wave–particle duality Matter wave

Qubit Qutrit Observable Probability distribution


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



Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)


Dirac Klein–Gordon Pauli Rydberg Schrödinger



Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Bayesian Quantum logic Relational Stochastic Scale relativity Transactional

Advanced topics

Fractional quantum mechanics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos Quantum gravity Perturbation theory (quantum mechanics) Density matrix Fractional quantum mechanics Scattering theory Quantum chaos Quantum statistical mechanics Quantum machine learning


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, while quantum mechanics is a comparatively recent invention. Classical mechanics
Classical mechanics
originated with Isaac Newton's laws of motion
Newton's laws of motion
in Philosophiæ Naturalis Principia Mathematica; Quantum Mechanics
was discovered in the early 20th century. Both are commonly held to constitute the most certain knowledge that exists about physical nature. Classical mechanics
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
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 the father of modern science, Galileo
brought together the ideas of other great thinkers of his time and began to analyze 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
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. 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[edit] 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
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
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[edit] 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[edit] Main articles: History of classical mechanics
History of classical mechanics
and History of quantum mechanics Antiquity[edit] Main article: Aristotelian mechanics The main theory of mechanics in antiquity was Aristotelian mechanics.[4] A later developer in this tradition is Hipparchus.[5] Medieval age[edit] Main article: Theory of impetus

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
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[edit] 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
Two New Sciences
(1638). Newton's 1687 Philosophiæ Naturalis Principia Mathematica
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[edit] 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[edit] 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[edit] 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[edit]

Play media

Prof. Walter Lewin
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
Analytical mechanics
is a reformulation of Newtonian mechanics
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
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[edit] The following are categorized 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 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 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[edit]

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[edit]

Applied mechanics Dynamics Engineering Index of engineering science and mechanics articles Kinematics Kinetics Non-autonomous mechanics Statics Wiesen Test of Mechanical Aptitude (WTMA)


^ Dugas, Rene. A History of Classical Mechanics. New York, NY: Dover Publications Inc, 1988, pg 19. ^ Rana, N.C., and Joag, P.S. Classical Mechanics. West Petal Nagar, New Delhi. Tata McGraw-Hill, 1991, pg 6. ^ Renn, J., Damerow, P., and McLaughlin, P. Aristotle, Archimedes, Euclid, and the Origin of Mechanics: The Perspective of Historical Epistemology. Berlin: Max Planck
Max Planck
Institute for the History of Science, 2010, pg 1-2. ^ "A history of mechanics". René Dugas (1988). p.19. ISBN 0-486-65632-2 ^ a b "A Tiny Taste of the History of Mechanics". The University of Texas at Austin. ^ Walter Lewin
Walter Lewin
(October 4, 1999). Work, Energy, and Universal Gravitation. MIT Course 8.01: Classical Mechanics, Lecture 11 (ogg) (videotape). Cambridge, MA US: MIT OCW. Event occurs at 1:21-10:10. Retrieved December 23, 2010. 

Further reading[edit]

Robert Stawell Ball
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 0-08-016739-X. CS1 maint: Multiple names: authors list (link)

External links[edit]

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

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Branches of physics


Applied Experimental Theoretical

Energy Motion

Thermodynamics Mechanics


Ballistics Lagrangian Hamiltonian

Continuum Celestial Statistical Solid Fluid Quantum

Waves Fields

Gravitation Electromagnetism Optics

Geometrical Physical Nonlinear Quantum

Quantum field theory Relativity

Special General

By speciality

Accelerator Acoustics Astrophysics

Nuclear Stellar Heliophysics


Space Astroparticle

Atomic–molecular–optical (AMO) Communication Computational Condensed matter

Mesoscopic Solid-state Soft

Digital Engineering Material Mathematical Molecular Nuclear Particle


Plasma Polymer Statistical

in life science


Virophysics Biomechanics

Medical physics

Cardiophysics Health physics Laser medicine Medical imaging‎ Nuclear medicine Neurophysics Psychophysics

with other sciences





Chemical Econophysics Geophysics