|
History Of Variational Principles In Physics
In physics, a variational principle is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional. Variational methods are exploited in many modern software applications to simulate matter and light. Since the development of analytical mechanics in the 18th century, the fundamental equations of physics have usually been established in terms of action principles, where the variational principle is applied to the action of a system in order to recover the fundamental equation of motion. This article describes the historical development of such action principles and other variational methods applied in physics. See History of physics for an overview and Outline of the history of physics for related histories. Antiquity Variational principles are found among earlier ideas in surveying and optics. The rope stretchers of ancient Egypt stretched corded ropes between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics Roadmap
Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the Mediterranean Sea *Classical architecture, architecture derived from Greek and Roman architecture of classical antiquity *Classical mythology, the body of myths from the ancient Greeks and Romans *Classical tradition, the reception of classical Greco-Roman antiquity by later cultures *Classics, study of the language and culture of classical antiquity, particularly its literature *Classicism, a high regard for classical antiquity in the arts Music and arts *Classical ballet, the most formal of the ballet styles *Classical music, a variety of Western musical styles from the 9th century to the present *Classical guitar, a common type of acoustic guitar *Classical Hollywood cinema, a visual and sound style in the American film industry between 1927 and 1963 *Classical Indian dance, various codified art forms whose theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Of Incidence (optics)
The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as optical, acoustic, microwave, and X-ray. In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams. In computer graphics and geography, the angle of incidence is also known as the illumination angle of a surface with a light source, such as the Earth's surface and the Sun. It can also be equivalently described as the angle between the tangent plane of the surface and another plane at right angles to the light rays. This means that the illumination angle of a certain point on Earth's surface is 0° if the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refraction
In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and Wind wave, water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. Optical Prism (optics), prisms and Lens (optics), lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light,R. Paschotta, article ochromatic dispersion in th, accessed on 2014-09-08 and thus the angle of the refraction also varies correspondingly. This is called dispersion (optics), dispersion and causes prism (optics), prisms and rainbows to divide white light into its constituent spectral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Principle
Fermat's principle, also known as the principle of least time, is the link between geometrical optics, ray optics and physical optics, wave optics. Fermat's principle states that the path taken by a Ray (optics), ray between two given points is the path that can be traveled in the least time. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the Snell's law, ordinary law of refraction of light (Fig.1), Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves. If points ''A'' and ''B'' are given, a wavefront expanding from ''A'' sweeps all possible ray paths radiating from ''A'', whether they pass through ''B'' or not. If the wavefront reaches point ''B'', it sweeps not only the ''ray'' path(s) from ''A'' to ''B'', but also an infinitude of near ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre De Fermat
Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' ''Arithmetica''. He was also a lawyer at the ''parlement'' of Toulouse, France. Biography Fermat was born in 1601 in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Dominique Fermat, was a wealthy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert Principle
D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert, and Italian-French mathematician Joseph Louis Lagrange. D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing ''forces of inertia'' which, when added to the applied forces in a system, result in ''dynamic equilibrium''. D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities. The principle does not apply for irreversible displacements, such as sliding friction, and more general specification of the irreversibility is required. Statement of the principle The principle states that the sum of the differences between the forces acting on a system of massive particles and the time derivatives of the momenta of the system itself projected onto any v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Work
In mechanics, virtual work arises in the application of the '' principle of least action'' to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the study of the mechanics of deformable bodies. History The principle of virtual work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, and R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Le Rond D'Alembert
Jean-Baptiste le Rond d'Alembert ( ; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie''. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French. Early years Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cornelius Lanczos
__NOTOC__ Cornelius (Cornel) Lanczos (, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-Jewish, Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians. Biography He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Jewish parents, Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable ... I gladly accept the honorable dedication."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'', American Mathematical Society In 1924 he discovered an exact solution of the Einste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Varignon
Pierre Varignon (; 1654 – 23 December 1722) was a French mathematician. He was educated at the Society of Jesus, Jesuit College and the University of Caen, where he received his Magister Artium, M.A. in 1682. He took Holy Orders the following year. Varignon gained his first exposure to mathematics by reading Euclid and then René Descartes, Descartes' ''La Géométrie''. He became professor of mathematics at the Collège des Quatre-Nations, Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year. In 1704, he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège de France, Collège Royal. He was elected to the Prussian Academy of Sciences, Berlin Academy in 1713 and to the Royal Society in 1718. Many of his works were published in Paris in 1725, three years after his death. His lectures at Mazarin were published in Elements de mathematique' in 1731. Varignon was a friend of Isaa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johann Bernoulli
Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educating Leonhard Euler in the pupil's youth. Biography Early life Johann was born in Basel, the son of Nicolaus Bernoulli, an apothecary, and his wife, Margarethe Schongauer, and began studying medicine at University of Basel. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli did not like business and convinced his father to allow him to study medicine instead. Johann Bernoulli began studying mathematics on the side with his older brother Jacob Bernoulli. Throughout Johann Bernoulli's education at Basel University, the Bernoulli brothers worked together, spending much of their time studying the newly discovered infinitesimal calculus. They were among t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Virtual Work
A principle may relate to a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning. They provide a guide for behavior or evaluation. A principle can make values explicit, so they are expressed in the form of rules and standards. Principles unpack the values underlying them more concretely so that the values can be more easily operationalized in policy statements and actions. In law, higher order, overarching principles establish rules to be followed, modified by sentencing guidelines relating to context and proportionality. In science and nature, a principle may define the essential characteristics of the system, or reflect the system's designed purpose. The effective operation would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 ''Principles of Operation''. It is important to differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
