mechanics

 

branch of physics concerned with motion and the forces that tend to cause it; it includes study of the mechanical properties of matter, such as density, elasticity, and viscosity. Mechanics may be roughly divided into statics and dynamics; statics deals with bodies at rest and is concerned with such topics as buoyancy, equilibrium, and the principles of simple machines, while dynamics deals with bodies in motion and is sometimes further divided into kinematics (description of motion without regard to its cause) and kinetics (explanation of changes in motion as a result of forces). A recent subdiscipline of dynamics is nonlinear dynamics, the study of systems in which small changes in a variable may have large effects. The science of mechanics may also be broken down, according to the state of matter being studied, into solid mechanics and fluid mechanics. The latter, the mechanics of liquids and gases, includes hydrostatics, hydrodynamics, pneumatics, aerodynamics, and other fields.

Early Mechanics

Mechanics was studied by a number of ancient Greek scientists, most notably Aristotle, whose ideas dominated the subject until the late Middle Ages, and Archimedes, who made several contributions and whose approach was quite modern compared to other ancient scientists. In the Aristotelian view, ordinary motion required a material medium; a body was kept in motion by the medium rushing in behind it in order to prevent a vacuum, which, according to this philosophy, could not occur in nature. Celestial bodies, on the other hand, were kept in motion through the vacuum of space by various agents that, in the Christianized version of Aquinas and others, acquired an angelic character.

This explanation was rejected in the 14th cent. by several philosophers, who revived the impetus theory proposed by John Philoponos in the 6th cent. A.D.; according to this theory a body acquired a quantity called impetus when it was set in motion, and it eventually came to rest as the impetus died out. The impetus school flourished in Paris and elsewhere during the 14th and 15th cent. and included William of Occam (Ockham), Jean Buridan, Albert of Saxony, Nicolas Oresme, and Nicolas of Cusa, although it was never successful in replacing the dominant Aristotelian mechanics.

Modern Mechanics

Modern mechanics dates from the work of Galileo, Simon Stevin, and others in the late 16th and early 17th cent. By means of experiment and mathematical analysis, Galileo made a number of important studies, particularly of falling bodies and projectiles. He enunciated the principle of inertia and used it to explain not only the mechanics of bodies on the earth but also that of celestial bodies (which, however, he believed moved in uniform circular orbits). The philosopher René Descartes advocated the application of the mathematical-mechanical approach to all fields and founded the mechanistic philosophy that was so important in science for the next two centuries or more.

The first system of modern mechanics to explain successfully all mechanical phenomena, both terrestrial and celestial, was that of Isaac Newton, who in his Principia (Mathematical Principles of Natural Philosophy, 1687) derived three laws of motion and showed how the principle of universal gravitation can be used to explain both the behavior of falling bodies on the earth and the orbits of the planets in the heavens. Newton's system of mechanics was developed extensively over the next two centuries by many scientists, including Johann and Daniel Bernoulli, Leonhard Euler, J. le Rond d'Alembert, J. L. Lagrange, P. S. Laplace, S. D. Poisson, and W. R. Hamilton. It found application to the explanation of the behavior of gases and thermodynamics in the statistical mechanics of J. C. Maxwell, Ludwig Boltzmann, and J. W. Gibbs.

In 1905, Albert Einstein showed that Newton's mechanics was an approximation, valid for cases involving speeds much less than the speed of light; for very great speeds the relativistic mechanics of his theory of relativity was required. Einstein showed further in his general theory of relativity (1916) that gravitation could be explained in terms of the effect of a massive body on the framework of space and time around it, this effect applying not only to the motions of other bodies possessing mass but also to light. In the quantum mechanics developed during the 1920s as part of the quantum theory, the motions of very tiny particles, such as the electrons in an atom, were explained using the fact that both matter and energy have a dual nature—sometimes behaving like particles and other times behaving like waves. Two different but mathematically equivalent forms of quantum mechanics were elaborated, the wave mechanics of Erwin Schrödinger and the matrix mechanics of Werner Heisenberg.

Bibliography

See I. B. Cohen, Introduction to Newton's Principia (1971); E. Mach, Science of Mechanics (6th ed. 1973); J. Gleick, Chaos (1987).

Mechanics (Greek Μηχανική) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment.

The discipline has its roots in several ancient civilizations: ancient Greece, where Aristotle studied the way bodies behaved when they were thrown through the air (e.g. a stone); ancient China, with figures such as Zhang Heng, Shen Kuo, and Su Song; and ancient India, with thinkers such as Kanada, Aryabhata, and Brahmagupta. During the Middle Ages, significant contributions to mechanics were made by Muslim scientists, such as Muhammad ibn Musa, Alhacen, Avicenna, Avempace, al-Baghdadi, and al-Khazini. During the early modern period, scientists such as Galileo, Kepler, and especially Newton, laid the foundation for what is now known as Newtonian mechanics.

A person working in the discipline is known as a mechanician.

Significance

Mechanics is the original discipline of physics, dealing with the macroscopic world that humans perceive. It is therefore a huge body of knowledge about the natural world. Mechanics encompasses the movement of all matter in the universe under the four fundamental interactions (or forces): gravity, the strong and weak interactions, and the electromagnetic interaction.

Mechanics also constitutes a central part of technology, the application of physical knowledge for humanly defined purposes. In this connection, the discipline is often known as engineering or applied mechanics. In this sense, mechanics is used to design and analyze the behavior of structures, mechanisms, and machines. Important aspects of the fields of mechanical engineering, aerospace engineering, civil engineering, structural engineering, materials engineering, biomedical engineering and biomechanics were spawned from the study of mechanics.

Classical vs. Quantum

The major division of the mechanics discipline separates classical mechanics from quantum mechanics.

Historically, classical mechanics came first, while quantum mechanics is a comparatively recent invention. Classical mechanics is older than written history, while quantum mechanics didn't appear until 1900. 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 relentless use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them.

Quantum mechanics is, formally at least, of the widest scope, and can be seen as encompassing 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. While it is true that historically quantum mechanics has been seen as having superseded classical mechanics, this is only true on the hypothetical or foundational level. For practical problems, classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.

Einsteinian vs. Newtonian

Analogous to the quantum vs. classical reformation, Einstein's general and special theories of relativity have expanded the scope of mechanics beyond the mechanics of Newton and Galileo, and made small corrections to them. Relativistic corrections were also needed for quantum mechanics, although relativity is categorized as a classical theory.

There are no contradictions or conflicts between the two, so long as the specific circumstances are carefully kept in mind. Just as one could, in the loosest possible sense, characterize classical mechanics as dealing with "large" bodies (such as engine parts), and quantum mechanics with "small" ones (such as particles), it could be said that relativistic mechanics deals with "fast" bodies, and non-relativistic mechanics with "slow" ones. However, "fast" and "slow" are subjective concepts, depending on the state of motion of the observer. This means that all mechanics, whether classical or quantum, potentially needs to be described relativistically. On the other hand, as an observer, one may frequently arrange the situation in such a way that this is not really required.

Types of Mechanical Bodies

Thus 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 analogous motions of an atomic nucleus are described by quantum mechanics.

Sub-disciplines in mechanics

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 mechanics

The following are described as forming Classical mechanics:

• Newtonian mechanics, the original theory of motion (kinematics) and forces (dynamics)
• Lagrangian mechanics, a theoretical formalism
• Hamiltonian mechanics, another theoretical formalism
• Celestial mechanics, the motion of stars, galaxies, etc.
• Astrodynamics, spacecraft navigation, etc.
• Solid mechanics, elasticity, the properties of (semi-)rigid bodies
• Acoustics, sound in solids, fluids, etc.
• Statics, semi-rigid bodies in mechanical equilibrium
• Fluid mechanics, the motion of fluids
• Continuum mechanics, mechanics of continua (both solid and fluid)
• Hydraulics, fluids in equilibrium
• Applied / Engineering mechanics
• Biomechanics, solids, fluids, etc. in biology
• Statistical mechanics, large assemblies of particles
• Relativistic or Einsteinian mechanics, universal gravitation

Quantum mechanics

The following are categorized as being part of Quantum mechanics:

• 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.
• Quantum statistical mechanics, large assemblies of particles

Professional Organizations

• Applied Mechanics Division, American Society of Mechanical Engineers
• Fluid Dynamics Division, American Physical Society

See also

• Applied Mechanics
• Engineering
• Physics

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

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