Mechanics

For other uses of the term, see Mechanic (disambiguation).

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.

Significance

Mechanics is the original discipline of physics and was formerly known as natural philosophy, dealing with forces and motion in the macroscopic world as the human eye perceives it. It has developed into a huge body of knowledge about important aspects of the natural world. Modern 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 versus quantum

Classical mechanics

History · Timeline Fundamental concepts Space · Time · Mass · Force Energy · Momentum Formulations Newtonian mechanics Lagrangian mechanics Hamiltonian mechanics Branches Applied mechanics Celestial mechanics Continuum mechanics Geometric optics Statistical mechanics Scientists Galileo · Kepler · Newton Laplace · Hamilton · d'Alembert Cauchy · Lagrange · Euler

Quantum mechanics

${\Delta x}\,{\Delta p}\geq {\frac {\hbar }{2}}$

Uncertainty principle

Introduction to... Mathematical formulation of... Background Classical mechanics Old quantum theory Interference · Bra-ket notation Hamiltonian Fundamental concepts Quantum state · Wave function Superposition · Entanglement Measurement · Uncertainty Exclusion · Duality Decoherence · Ehrenfest theorem · Tunneling Experiments Double-slit experiment Davisson–Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Elitzur-Vaidman bomb-tester Formulations Schrödinger picture Heisenberg picture Interaction picture Matrix mechanics Sum over histories Equations Schrödinger equation Pauli equation Klein–Gordon equation Dirac equation Interpretations Copenhagen · Ensemble Hidden variable theory · Transactional Many-worlds · Consistent histories Quantum logic Advanced topics Quantum field theory Quantum gravity Theory of everything Scientists Planck · Einstein · Bohr · Sommerfeld · Kramers · Heisenberg· Born · Jordan · Pauli · Dirac · de Broglie ·Schrödinger · von Neumann · Wigner · Feynman · Bohm · Everett · Bell

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

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