Mechanics

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This article is about an area of scientific study. For other uses, see Mechanic (disambiguation).
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Classical mechanics
Second law of motion
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Quantum mechanics
Schrödinger equation
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Mechanics (from

displacements
, which are changes of an object's position relative to its environment.

Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes[4][5][6] (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics.

As a branch of classical physics, 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

Main articles: History of classical mechanics and History of quantum mechanics

Antiquity

Main article:
Aristotelian mechanics

The ancient

Aristotelian mechanics, 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

dynamically, an approach that may have been stimulated by prior work of the Pythagorean Archytas.[7] Examples of this tradition include pseudo-Euclid (On the Balance), Archimedes (On the Equilibrium of Planes, On Floating Bodies), Hero (Mechanica), and Pappus (Collection, Book VIII).[8][9]

Medieval age

Main article: Theory of impetus
Arabic machine in a manuscript of unknown date

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.

Persian Islamic polymath

air resistance to dissipate it.[10][11][12] 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.[10]

On the question of a body subject to a constant (uniform) force, the 12th-century Jewish-Arab scholar

motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]."[13]

Influenced by earlier writers such as Ibn Sina[12] and al-Baghdaadi,[14] the 14th-century French priest Jean Buridan developed the theory of impetus, which later 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. 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

First European depiction of a piston pump, by Taccola, c. 1450.[15]

Two central figures in the early modern age are

Newtonian mechanics.[9]

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 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

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 the three main designations consisting of various subjects that are studied in mechanics.

Note that there is also the "

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 article: Classical mechanics
Prof.
MIT course 8.01[16]

The following are described as forming classical mechanics:

Quantum

Main article: Quantum mechanics

The following are categorized as being part of quantum mechanics:

Historically, classical mechanics had been around for nearly a quarter millennium before quantum mechanics developed. Classical mechanics originated with Isaac Newton's laws of motion in Philosophiæ Naturalis Principia Mathematica, 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. 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 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

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 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

Main article: Relativistic mechanics

Akin to the distinction between quantum and classical mechanics,

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 Newtonian mechanics, the kinetic energy of a free particle is E = 1/2mv2, whereas in relativistic mechanics, it is E = (γ − 1)mc2 (where γ is the Lorentz factor; this formula reduces to the Newtonian expression in the low energy limit).[17]

For high-energy processes, quantum mechanics must be adjusted to account for special relativity; this has led to the development of quantum field theory.[18]

Professional organizations

See also

References

  1. ^ "mechanics". Oxford English Dictionary. 1933.
  2. ^ Henry George Liddell; Robert Scott (1940). "mechanics". A Greek-English Lexicon.
  3. OCLC 1104689918
    .
  4. ^ Dugas, Rene. A History of Classical Mechanics. New York, NY: Dover Publications Inc, 1988, pg 19.
  5. ^ Rana, N.C., and Joag, P.S. Classical Mechanics. West Petal Nagar, New Delhi. Tata McGraw-Hill, 1991, pg 6.
  6. ^ Renn, J., Damerow, P., and McLaughlin, P. Aristotle, Archimedes, Euclid, and the Origin of Mechanics: The Perspective of Historical Epistemology. Berlin: Max Planck Institute for the History of Science, 2010, pg 1-2.
  7. ISBN 978-0-19-928931-8
    .
  8. ISBN 0-486-65632-2
  9. ^ a b "A Tiny Taste of the History of Mechanics". The University of Texas at Austin.
  10. ^
    S2CID 250809354
    .
  11. ISBN 978-0-7007-0314-2
    .
  12. ^
    S2CID 84784804
    .
  13. ISBN 0-684-10114-9
    .
    (    cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History of Ideas 64 (4), p. 521-546 [528].)
  14. ISBN 90-04-13228-7
  15. ISBN 0-415-15291-7
    .
  16. ^ 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.
  17. ^ Landau, L.; Lifshitz, E. (January 15, 1980). The Classical Theory of Fields (4th Revised English ed.). Butterworth-Heinemann. p. 27.
  18. ISBN 0-521-67053-5
    .

Further reading

External links

Look up mechanics in Wiktionary, the free dictionary.
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