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Hamiltonian System A HAMILTONIAN SYSTEM is a dynamical system governed by Hamilton\'s equations . In physics , this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field . These systems can be studied in both Hamiltonian mechanics and dynamical systems theory . CONTENTS * 1 Overview * 2 Time independent Hamiltonian system * 2.1 Example * 3 Symplectic structure * 4 Examples * 5 See also * 6 References * 7 Further reading * 8 External links OVERVIEWInformally, a Hamiltonian system is a mathematical formalism developed by Hamilton to describe the evolution equations of a physical system. The advantage of this description is that it gives important insight about the dynamics, even if the initial value problem cannot be solved analytically [...More...]  "Hamiltonian System" on: Wikipedia Yahoo 

Divergence Theorem In vector calculus , the DIVERGENCE THEOREM, also known as GAUSS\'S THEOREM or OSTROGRADSKY\'S THEOREM, is a result that relates the flow (that is, flux ) of a vector field through a surface to the behavior of the vector field inside the surface. More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that the sum of all sources (with sinks regarded as negative sources) gives the net flux out of a region. The divergence theorem is an important result for the mathematics of physics and engineering , in particular in electrostatics and fluid dynamics . In physics and engineering, the divergence theorem is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus [...More...]  "Divergence Theorem" on: Wikipedia Yahoo 

Nbody Problem In physics , the NBODY PROBLEM is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally . Solving this problem has been motivated by the desire to understand the motions of the Sun Sun , Moon Moon , planets and the visible stars . In the 20th century, understanding the dynamics of globular cluster star systems became an important nbody problem. The nbody problem in general relativity is considerably more difficult to solve. The classical physical problem can be informally stated as: Given the quasisteady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times. To this purpose the twobody problem has been completely solved and is discussed below; as is the famous restricted threebody Problem [...More...]  "Nbody Problem" on: Wikipedia Yahoo 

Identity Matrix In linear algebra , the IDENTITY MATRIX, or sometimes ambiguously called a UNIT MATRIX, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics , the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.) Less frequently, some mathematics books use U or E to represent the identity matrix, meaning "unit matrix" and the German word "Einheitsmatrix", respectively [...More...]  "Identity Matrix" on: Wikipedia Yahoo 

Simple Harmonic Motion In mechanics and physics , SIMPLE HARMONIC MOTION is a type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement . Simple harmonic motion can serve as a mathematical model for a variety of motions, such as the oscillation of a spring . In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration . Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke\'s Law . The motion is sinusoidal in time and demonstrates a single resonant frequency. For simple harmonic motion to be an accurate model for a pendulum, the net force on the object at the end of the pendulum must be proportional to the displacement. This is a good approximation when the angle of the swing is small [...More...]  "Simple Harmonic Motion" on: Wikipedia Yahoo 

Constant Of Motion In mechanics , a CONSTANT OF MOTION is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint, the natural consequence of the equations of motion , rather than a physical constraint (which would require extra constraint forces ). Common examples include specific energy , specific linear momentum , specific angular momentum and the Laplace–Runge–Lenz vector (for inversesquare force laws ). CONTENTS * 1 Applications * 2 Methods for identifying constants of motion * 3 In quantum mechanics * 3.1 Derivation * 3.2 Comment * 3.3 Derivation * 4 Relevance for quantum chaos * 5 Integral of motion * 6 Dirac observables * 7 References APPLICATIONSConstants of motion are useful because they allow properties of the motion to be derived without solving the equations of motion [...More...]  "Constant Of Motion" on: Wikipedia Yahoo 

Pendulum A PENDULUM is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position , it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period . The period depends on the length of the pendulum and also to a slight degree on the amplitude , the width of the pendulum's swing. From the first scientific investigations of the pendulum around 1602 by Galileo Galilei , the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s [...More...]  "Pendulum" on: Wikipedia Yahoo 

Cambridge Univ. Press CAMBRIDGE UNIVERSITY PRESS (CUP) is the publishing business of the University of Cambridge University of Cambridge . Granted letters patent by Henry VIII Henry VIII in 1534, it is the world's oldest publishing house and the secondlargest university press in the world (after Oxford University Press Oxford University Press ). It also holds letters patent as the Queen\'s Printer . The Press's mission is "To further the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence." Cambridge Cambridge University Press is a department of the University of Cambridge Cambridge and is both an academic and educational publisher . With a global sales presence, publishing hubs, and offices in more than 40 countries , it publishes over 50,000 titles by authors from over 100 countries [...More...]  "Cambridge Univ. Press" on: Wikipedia Yahoo 

American Mathematical Society The AMERICAN MATHEMATICAL SOCIETY (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics Mathematics and a member of the Conference Board of the Mathematical Sciences . CONTENTS * 1 History * 2 Meetings * 3 Fellows * 4 Publications * 5 Prizes * 6 Typesetting * 7 Presidents * 7.1 1888–1900 * 7.2 1901–1950 * 7.3 1951–2000 * 7.4 2001–present * 8 See also * 9 References * 10 External links HISTORYIt was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske , who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary [...More...]  "American Mathematical Society" on: Wikipedia Yahoo 

Scholarpedia SCHOLARPEDIA is an Englishlanguage online wiki based encyclopedia with features commonly associated with openaccess online academic journals , which aims to have quality content. Scholarpedia Scholarpedia articles are written by invited expert authors and are subject to peer review . Scholarpedia Scholarpedia lists the real names and affiliations of all authors, curators and editors involved in an article: however, the peer review process (which can suggest changes or additions, and has to be satisfied before an article can appear) is anonymous. Scholarpedia Scholarpedia articles are stored in an online repository, and can be cited as conventional journal articles ( Scholarpedia Scholarpedia has the ISSN ISSN number ISSN ISSN 19416016 ). Scholarpedia's citation system includes support for revision numbers [...More...]  "Scholarpedia" on: Wikipedia Yahoo 

Special SPECIAL or SPECIALS may refer to: CONTENTS * 1 Music * 2 Film and television * 3 Other uses * 4 See also MUSIC * Special (album) , a 1992 album by Vesta Williams * "Special" (Garbage song) , 1998 * "Special" (Mew song) , 2005 * "Special" (Stephen Lynch song) , 2000 * The Specials The Specials , a British band * "Special", a song by Violent Femmes on The Blind Leading the Naked * "Special", a song on [...More...]  "Special" on: Wikipedia Yahoo 

Imperial College Press IMPERIAL COLLEGE PRESS (ICP) was formed in 1995 as a partnership between Imperial College Imperial College of Science, Technology and Medicine Medicine in London and World Scientific publishing. This publishing house was awarded the rights, by The Nobel Foundation , Sweden Sweden , to publish The Nobel Prize: The First 100 years, edited by Agneta Wallin Levinovitz and Nils Ringertz [...More...]  "Imperial College Press" on: Wikipedia Yahoo 

Springer Science+Business Media SPRINGER SCIENCE+BUSINESS MEDIA or SPRINGER, part of Springer Nature since 2015, is a global publishing company that publishes books, ebooks and peerreviewed journals in science, technical and medical (STM) publishing. Springer also hosts a number of scientific databases, including SpringerLink, Springer Protocols Springer Protocols , and SpringerImages. Book publications include major reference works, textbooks, monographs and book series; more than 168,000 titles are available as ebooks in 24 subject collections. Springer has major offices in Berlin Berlin , Heidelberg Heidelberg , Dordrecht Dordrecht , and New York City New York City . On 15 January 2015, Holtzbrinck Publishing Publishing Group / Nature Publishing Group and Springer Science+Business Media Springer Science+Business Media announced a merger [...More...]  "Springer Science+Business Media" on: Wikipedia Yahoo 

World Scientific WORLD SCIENTIFIC PUBLISHING is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore Singapore . The company was founded in 1981. It publishes about 500 books annually as well as more than 150 journals in various fields. In 1995, World Scientific cofounded the Londonbased Imperial College Press together with the Imperial College of Science, Technology and Medicine . CONTENTS* 1 Company structure * 1.1 Imperial College Press * 2 Controversy * 3 See also * 4 References * 5 External links COMPANY STRUCTUREThe company head office is in Singapore Singapore . The Chairman and EditorinChief is Phua Kok Khoo , while the Managing Director is Doreen Liu . The company was cofounded by them in 1981 [...More...]  "World Scientific" on: Wikipedia Yahoo 

Evolution Equation TIME EVOLUTION is the change of state brought about by the passage of time , applicable to systems with internal state (also called stateful systems). In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite. In classical physics , time evolution of a collection of rigid bodies is governed by the principles of classical mechanics . In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by Newton\'s laws of motion . These principles can also be equivalently expressed more abstractly by Hamiltonian mechanics or Lagrangian mechanics . The concept of time evolution may be applicable to other stateful systems as well [...More...]  "Evolution Equation" on: Wikipedia Yahoo 

Harmonic Oscillator In classical mechanics , a HARMONIC OSCILLATOR is a system that, when displaced from its equilibrium position, experiences a restoring force , F, proportional to the displacement, x: F = k x {displaystyle {vec {F}}=k{vec {x}},} where k is a positive constant . If F is the only force acting on the system, the system is called a SIMPLE HARMONIC OSCILLATOR, and it undergoes simple harmonic motion : sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude) [...More...]  "Harmonic Oscillator" on: Wikipedia Yahoo 