mechanics

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.

Branch of physics that combines the principles and procedures of statistics with the laws of both classical mechanics and quantum mechanics. It considers the average behaviour of a large number of particles rather than the behaviour of any individual particle, drawing heavily on the laws of probability, and aims to predict and explain the measurable properties of macroscopic (bulk) systems on the basis of the properties and behaviour of their microscopic constituents.

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Study of soils and their utilization, especially in planning foundations for structures and highways. How the soil of a given site will support the weight of structures or respond to movement in the course of construction depends on a number of properties (e.g., compressibility, elasticity, and permeability). Examination techniques include trench-digging, boring, and pumping samples to the surface with water. Seismic testing and measurement of electrical resistance also yield helpful information. In road construction, soil mechanics helps determine which type of pavement (rigid or flexible) will last longer. The study of soil characteristics is also used to choose the most suitable method for excavating underground tunnels. Seealso foundation, settling.

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Branch of mathematical physics that deals with atomic and subatomic systems. It is concerned with phenomena that are so small-scale that they cannot be described in classical terms, and it is formulated entirely in terms of statistical probabilities. Considered one of the great ideas of the 20th century, quantum mechanics was developed mainly by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, and Max Born and led to a drastic reappraisal of the concept of objective reality. It explained the structure of atoms, atomic nuclei (see nucleus), and molecules; the behaviour of subatomic particles; the nature of chemical bonds (see bonding); the properties of crystalline solids (see crystal); nuclear energy; and the forces that stabilize collapsed stars. It also led directly to the development of the laser, the electron microscope, and the transistor.

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Science of the action of forces on material bodies. It forms a central part of all physical science and engineering. Beginning with Newton's laws of motion in the 17th century, the theory has since been modified and expanded by the theories of quantum mechanics and relativity. Newton's theory of mechanics, known as classical mechanics, accurately represented the effects of forces under all conditions known in his time. It can be divided into statics, the study of equilibrium, and dynamics, the study of motion caused by forces. Though classical mechanics fails on the scale of atoms and molecules, it remains the framework for much of modern science and technology.

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Study of the effects of forces and energy on liquids and gases. One branch of the field, hydrostatics, deals with fluids at rest; the other, fluid dynamics, deals with fluids in motion and with the motion of bodies through fluids. Liquids and gases are both treated as fluids because they often have the same equations of motion and exhibit the same flow phenomena. The subject has numerous applications in fields varying from aeronautics and marine engineering to the study of blood flow and the dynamics of swimming.

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Branch of astronomy that deals with the mathematical theory of the motions of celestial bodies. Johannes Kepler's laws of planetary motion (1609–19) and Newton's laws of motion (1687) are fundamental to it. In the 18th century, powerful methods of mathematical analysis were generally successful in accounting for the observed motions of bodies in the solar system. One branch of celestial mechanics deals with the effect of gravitation on rotating bodies, with applications to Earth (see tide) and other objects in space. A modern derivation, called orbital mechanics or flight mechanics, deals with the motions of spacecraft under the influence of gravity, thrust, atmospheric drag, and other forces; it is used to calculate trajectories for ascent into space, achieving orbit, rendezvous, descent, and lunar and interplanetary flights.

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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 (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and especially Newton, laid the foundation for what is now known as classical mechanics.

Classical versus 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 originated with Isaac Newton's Laws of motion in Principia Mathematica, 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 of a wider 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. Quantum mechanics has superseded classical mechanics at foundational level and is indispensable for the explanation and prediction of processes at molecular and (sub)atomic level. However, for macroscopical processes classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.

Einsteinian versus Newtonian

Analogous to the quantum versus 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 fundamental corrections to them, that become significant and even dominant as speeds of material objects approach the speed of light, which cannot be exceeded. Relativistic corrections are also needed for quantum mechanics, although relativity has not been fully integrated with it yet; this is one of the hurdles that has to be overcome in developing a Grand Unified Theory.

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, based on the principle of conservation of energy
• Hamiltonian mechanics, another theoretical formalism, based on the principle of the least action
• Celestial mechanics, the motion of heavenly bodies: planets, comets, stars, galaxies, etc.
• Astrodynamics, spacecraft navigation, etc.
• Solid mechanics, elasticity, the properties of (semi-)rigid bodies
• 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 / Engineering mechanics
• Biomechanics, solids, fluids, etc. in biology
• Biophysics, physical processes in living organisms
• Statistical mechanics, assemblies of particles too large to be described in a deterministic way
• 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
• 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.

See also

• Analytical mechanics
• Applied mechanics
• Dynamics
• Engineering
• Kinematics
• Kinetics

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