
Review of Short Phrases and Links 
This Review contains major "Mechanics" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.
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 Fluid mechanics is a branch of physics that describes the behavior of fluids (which include liquids and gases).
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 Geomechanics (Greek prefix geo meaning earth; and mechanics) is the study of the behavior of soil and rock.
 In mechanics, the twobody problem is a special case of the nbody problem that admits a closed form solution.
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 Fluid mechanics (also called fluid dynamics) is the study of fluids, that is liquids and gases.
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 For his work on antiparticles and wave mechanics, he received the Nobel Prize in physics in 1933.
 When quantum mechanics was developed, it was seen to be a relation between the classical and quantum descriptions of a system using wave mechanics.
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 The Austrian physicist Erwin SchrÃ¶dinger (18871961) was the founder of wave mechanics and described the quantum behavior of electrons.
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 In 1926 he developed a version of quantum mechanics, which included “Matrix Mechanics” and “Wave Mechanics” as special cases.
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 Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.
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 An electron is described by its energy in Bohr's atom which was carried over to matrix mechanics.
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 Feynman diagram and path integral methods are also used in statistical mechanics.
 The direct approach shows that the expectation values calculated from the path integral reproduce the usual ones of quantum mechanics.
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 He is recognized for his successful work in a variety of fields including, thermodynamics, optics, statistical mechanics, and physical chemistry.
 He proposed the theory of relativity and also made major contributions to the development of quantum mechanics, statistical mechanics and cosmology.
 Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, statistical mechanics, and spectroscopy.
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 This textbook gives a clear and thorough presentation of the fundamental principles of mechanics and strength of materials.
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 As a general introduction to QFT, without the maths, nor attempting to be a textbook, Dirac  'Lectures on Quantum Mechanics ' is a good book.
 A textbook on numerical physics, covering classical mechanics, electrodynamics, optics, statistical physics and quantum mechanics.
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 Recognition and description of deformed rocks, map reading, and an introduction to the mechanics and patterns of deformation.
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 Another theme is the description of various approaches to Bohmian mechanics and their role in quantum mechanics and general relativity.
 The physical description of electromagnetism has since been combined with quantum mechanics into the theory of quantum electrodynamics.
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 In 1901 Prandtl became a professor of mechanics at a technical school in Hannover.
 He was a professor of mathematics and mechanics and chess took second place to his professional life.
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 In 1834, through the good offices of Poisson, Cournot found a permanent appointment as professor of analysis and mechanics at Lyon.
 For example, physicists have tried for most of the last century to invent a theory which described gravity while being consistent with quantum mechanics.
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 In 1930, Paul Dirac developed the first description of the electron that was consistent with both quantum mechanics and special relativity.
 However, the principles of quantum mechanics can and have been extended into quantum field theories, which are consistent with special relativity.
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 For researchers in mathematics, mathematical physics, computer algebra, control theory and theoretical mechanics.
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 It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory.
 Stiff problems are ubiquitous in chemical kinetics, control theory, solid mechanics, weather prediction, biology, and electronics.
 Linus Pauling was considered to be the father of molecular biology, implementing the science of Quantum Mechanics with that of biology.
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 In practice, biology and quantum mechanics work together and complement each other.
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 This book will be of interest to students of fluid mechanics, turbulence, and vortex methods as well as to applied mathematicians and engineers.
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 Celestial mechanics has become an essential tool as scientists and engineers navigate manned and unmanned spacecraft throughout the solar system.
 Quantum mechanics has given scientists and engineers a new and deeper understanding of physical reality.
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 This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.
 The fundamental lesson of general relativity is that there is no fixed spacetime background, as found in Newtonian mechanics and special relativity.
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 Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5557 seconds of arc per century.
 Newton's notation is mainly used in mechanics, normally for time derivatives such as velocity and acceleration, and in ODE theory.
 In classical mechanics, a velocity v reverses under the operation of T, but an acceleration does not.
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 Classically, the state of an object is just its state of motion, described completely in Newtonian mechanics by its position and velocity.
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 Fluid mechanics can be further split into fluid statics and fluid dynamics, and is itself a subdiscipline of continuum mechanics.
 In fluid mechanics or more generally continuum mechanics, an incompressible flow is solid or fluid flow in which the divergence of velocity is zero.
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 Fluid dynamics is a mathematical discipline within continuum mechanics, dealing with fluid flows.
 He laid the foundations for a new branch of physics known as Quantum mechanics and was awarded the 1932 Nobel Prize for his work.
 The branch of physics which studies this is statistical mechanics or thermodynamics.
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 In this view, Statistical Mechanics, and therefore Thermodynamics, is not a physical theory at all, but rather is a branch of Information Theory.
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 Engineering and innovation Isaac Newton, promulgator of universal gravitation, Newtonian mechanics and infinitesimal calculus.
 Contains his thoughts on Euclidean geometry, manipulations of series, functions and foundations of calculus, and topics in mechanics.
 Physics makes particular use of calculus; all concepts in classical mechanics and electromagnetism are interrelated through calculus.
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 When he was 13, he had mastered the calculus and other forms of analytical mechanics, his father Farkas Bolyai giving him instructions.
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 Extensions of the action principle describe relativistic mechanics, quantum mechanics, electricity and magnetism.
 His current interests lie in the theory of topological phases, frustrated magnetism, and the statistical mechanics of quantum computation.
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 Statistical mechanics has also yielded deep insights in the understanding of magnetism, phase transitions, and superconductivity.
 I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students.
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 It includes Poisson's work on the applications of mathematics to topics such as electricity, magnetism and mechanics.
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 The chemical level is described by quantum mechanics and the laws of electricity and magnetism, from which there emerge atomic and molecular behavior.
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 Game mechanics Main article: Game mechanics (Dungeons & Dragons) D&D uses polyhedral dice to resolve random events.
 New Game Mechanics  BioShock 2 contains many new gameplay mechanics.
 I do like the game mechanics of d20 but in this I chose Star Wars because of the fact it's Star Wars.
 If you want lots of rules but minimal "narrative" or "meta" mechanics, you could always get the GURPS and its steampunk supplement.
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 Despite their generally collaborative nature, roleplaying games have rules known usually as game mechanics.
 While the SRD presents a distinctly fantasythemed set of rules, the mechanics which it outlines were designed to be adaptable to nearly any genre.
 CELESTIAL MECHANICS. *Johannes Kepler* made no bones about his faith.
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 The principles of orbital mechanics were first discovered and explained by Johannes Kepler in the 17th century.
 Tom Van Flandern received his Ph.D. degree in Astronomy, specializing in celestial mechanics (the theory of orbits), from Yale University in 1969.
 Orbital mechanics (astrodynamics) is a subfield which focuses on the orbits of artificial satellites.
 This article is about orbits in celestial mechanics, due to gravity.
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 It can be plausibly argued that physics began with mechanics  the science of machines, forces and motion.
 Celestial mechanics and astrodynamics are two distinct subjects, the one science, as has been said, the other engineering (as in spaceflight, for example).
 As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science.
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 In modern fluid mechanics the role of vortex dynamics in explaining flow phenomena is firmly established.
 It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena.
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 Differential equations are used to construct mathematical models of physical phenomena such as fluid dynamics or celestial mechanics.
 Modern quantum mechanics was born in 1925, when Heisenberg developed matrix mechanics and SchrÃ¶dinger invented wave mechanics and the SchrÃ¶dinger equation.
 Matrix mechanics rapidly developed into modern quantum mechanics, and gave interesting physical results on the spectra of atoms.
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 This formulation is a form of second quantization, but it predates modern quantum mechanics.
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 Keywords: mathematics, mathematical physics, theoretical mechanics, probability, mathematical statistics, mathematical biology.
 In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape.
 Boltzmann worked on statistical mechanics using probability to describe how the properties of atoms determine the properties of matter.
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 The ideal gas model has been explored in both the Newtonian dynamics (as in " kinetic theory ") and in quantum mechanics (as a " gas in a box ").
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 In 1857 Rudolf Clausius, a German physicist, clarified the mechanics of evaporation in his kinetic theory of gases.
 The theory of gases From the middle of the 19 th century the error distribution was used in the theory of gases (and later statistical mechanics).
 In analytical mechanics the conservation of momentum is a consequence of translational invariance of Lagrangian in the absence of external forces.
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 In quantum mechanics, the conservation of probability also yields a continuity equation.
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 Liouville's theorem is interpreted as the conservation of phase volume in Hamiltonian systems, which is the basis for classical statistical mechanics.
 He laid the foundation for the theory of symmetries in quantum mechanics.
 The goal of Hamiltonian mechanics is to encode the symmetries of in the Lie algebra.
 This is the group of symmetries of classical mechanics.
 Quantum mechanics is described according to von Neumann, and the theory of symmetry is described according to Wigner.
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 The second aspect is that of symmetry which plays a much greater role in quantum mechanics than in classical mechanics.
 This transition also provides an important insight into why the mathematics of symmetry are so deeply intertwined with those of quantum mechanics.
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 This book is an introduction to both the theory of group representations and its applications in quantum mechanics.
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 This book on the new foundations for classical mechanics (second edition) was written as an introduction to geometric algebra.
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 This book is an introduction to celestial mechanics.
 Researchers, practitioners and students in geomechanics, mechanics of solids, soil and rock engineering will find this book an invaluable reference.
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 The book also includes a description of the physical mechanics of the prayer wheel and some thoughts as to how one might make one's own.
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 This is a book for people who want to use functional analysis to justify approximate methods in Mechanics and Inverse Problems.
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 They have applications in areas of applied mathematics as diverse as economics and quantum mechanics.
 He wrote on vision, mathematics, Newtonian mechanics, economics, and medicine as well as philosophy.
 Explaining the behavior of the electron "orbits" was one of the driving forces behind the development of quantum mechanics.
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 Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior of a wide range of physical systems.
 Think, for example, of the development of quantum mechanics, the physics that studies the behavior of atoms and molecules.
 Introduces the basics of the shell model of the nucleus and a beginning discussion of quantum mechanics.
 Quantum mechanics (QM) is a branch of physics describing the behavior of energy and matter at the atomic and subatomic scales.
 In quantum mechanics, spin is particularly important for systems at atomic length scales, such as individual atoms, protons, or electrons.
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 Quantum mechanics is a fundamental physical theory which extends and corrects Newtonian mechanics, especially at the atomic and subatomic levels.
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 The kinetic theory of gases uses statistical mechanics to relate this motion to the average kinetic energy of atoms and molecules in the system.
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 This difficulty highlights the fact that quantum "mechanics" applied to atoms is a theory without physical reality.
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 Quantum mechanics is the description of physics at the scale of atoms, and the even smaller scales of fundamental particles.
 In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.
 An atomic orbital is the description of the behavior of an electron in an atom according to quantum mechanics.
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 Explaining the behavior of the electrons that "orbit" an atom was one of the driving forces behind the development of quantum mechanics.
 The kvector, in quantum mechanics, is the representation of the momentum of a particle.
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 However, in quantum mechanics, where a light wave can act like a particle, a gamma ray striking an electron gives it a kick.
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 To unify gravity, relativity and quantum mechanics was already beyond my highest aspirations for what the K particle could possibly achieve.
 Matrix mechanics introduced infinite matrices to represent the position and momentum of an electron inside an atom.
 Hence, conservation of momentum Momentum In classical mechanics, momentum is the product of the mass and velocity of an object.
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 It is basic to the teaching of Newtonian mechanics that momentum is conserved when energy transfers between particles in motion.
 While Heisenberg proposed to develop Quantum Mechanics by considering that the concept of trajectory could not be kept in the theory.
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 In quantum statistical mechanics, the concept of entropy was developed by John von Neumann and is generally referred to as "von Neumann entropy".
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 Kinetic energy, a concept of mechanics, is the product of mass and the square of a particle's velocity.
 An elegant explanation of quantum mechanics and relativity paves the way for an understanding of the laws that govern particle physics.
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 Again, the current incompatibility of general relativity and quantum mechanics at electron scales prevents us from understanding why this never occurs.
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 At the center of the play (and at the center of our understanding of the world through quantum mechanics) is a fundamental uncertainty.
 After Newton, classical mechanics became a principal field of study in mathematics as well as physics.
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 And it is a Hilbert space that mathematicians (and physicists, in quantum mechanics) generally want to study.
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 Percolation can be considered to be a branch of the study of dynamical systems or statistical mechanics.
 The latter, the mechanics of liquids and gases, includes hydrostatics, hydrodynamics, pneumatics, aerodynamics, and other fields.
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 Fluid mechanics is a field that spreads widely and to all fields of engineering, science and medicine.
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 Tensors are used also in other fields such as continuum mechanics.
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