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Laplace–Runge–Lenz Vector
In classical mechanics, the Laplace–Runge–Lenz (LRL) vector is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a binary star or a planet revolving around a star. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be '' conserved''. More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them; such problems are called Kepler problems. The hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse-square central force. The LRL vector was essential in the first quantum mechanical derivation of the spectrum of the hydrogen atom, before the development of the Schrö ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry (physics)
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuous'' (such as rotation of a circle) or '' discrete'' (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see ''Symmetry group''). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Of Energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. Classically, conservation of energy was distinct from conservation of mass. However, special relativity shows that mass is related to energy and vice versa by ''E = mc2'', and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). # The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or the observer. Origins and significance Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies".Albert Einstein (1905)''Zur Elektrodynamik bewegter Körper'', ''Annalen der Physik'' 17: 891; English translatioOn the Electrodynamics of Moving Bodiesby George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920). The in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity Vector
In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity and argument of periapsis parameters for which eccentricity zero (circular orbit) corresponds to a singularity. Calculation The eccentricity vector \mathbf \, is: : \mathbf = - = \left ( - \right ) \mathbf - \mathbf which follows immediately from the vector identity: : \mathbf\times \left ( \mathbf\times \mathbf \right ) = \left ( \mathbf \cdot \mathbf \right ) \mathbf - \left ( \mathbf \cdot \mathbf \right ) \mathbf where: *\mathbf\,\! is position vector *\mathbf\,\! is velocity vector * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stigler's Law Of Eponymy
Stigler's law of eponymy, proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication ''Stigler’s law of eponymy'', states that no scientific discovery is named after its original discoverer. Examples include Hubble's law, which was derived by Georges Lemaître two years before Edwin Hubble, the Pythagorean theorem, which was known to Babylonian mathematicians before Pythagoras, and Halley's Comet, which was observed by astronomers since at least 240 BC (although its official designation is due to the first ever mathematical prediction of such astronomical phenomenon in the sky, not to its discovery). Stigler himself named the sociologist Robert K. Merton as the discoverer of "Stigler's law" to show that it follows its own decree, though the phenomenon had previously been noted by others. Derivation Historical acclaim for discoveries is often assigned to persons of note who bring attention to an idea that is not yet widely known, whether o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Journal Of Physics
The ''American Journal of Physics'' is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics. The editor-in-chief is Beth Parks of Colgate University."Current Frequency: Monthly, 2002; and Former Frequency varies, 1940-2001" Confirmation of Editor, ISSN, CODEN, and other relevant information. Aims and scope The focus of this journal is undergraduate and graduate level physics. The intended audience is college and university physics teachers and students. Coverage includes current research in physics, instructional laboratory equipment, laboratory demonstrations, teaching methodologies, lists of resources, and book reviews. In addition, historical, philosophical and cultural aspects of physics are also covered. According to the 2021 Journal Citation Reports from Clarivate, this journal has a 2020 impact factor of 1.022. History The former title of this journal was ''American Physics Teache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Lenz
Wilhelm Lenz (February 8, 1888 in Frankfurt am Main – April 30, 1957 in Hamburg) was a German physicist, most notable for his invention of the Ising model and for his application of the Laplace–Runge–Lenz vector to the old quantum mechanical treatment of hydrogen-like atoms. Biography In 1906, Lenz graduated from the Klinger-Oberralschule, a non-classical secondary school in Frankfurt, and went to study mathematics and physics at the University of Göttingen. From 1908 to 1911, Lenz studied under Arnold Sommerfeld, at the University of Munich, and he was granted his doctorate on March 2, 1911. Upon graduation, he stayed on at the University, became Sommerfeld’s assistant on April 1, 1911, and he completed his Habilitation on February 20, 1914, becoming a Privatdozent on April 4, 1914. During World War I, he served as a radio operator in France and was awarded the Iron Cross Second Class in 1916. From September 30, 1920, he was again an assistant to Sommerfeld at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl David Tolmé Runge
Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist. He was co-developer and co-eponym of the Runge–Kutta method (German pronunciation: ), in the field of what is today known as numerical analysis. Life and work Runge spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. His mother was Fanny Schwartz Tolmé. The family later moved to Bremen, where his father died early (in 1864). In 1880, he received his Ph.D. in mathematics at Berlin, where he studied under Karl Weierstrass. In 1886, he became a professor at the Technische Hochschule Hannover in Hanover, Germany. His interests included mathematics, spectroscopy, geodesy, and astrophysics. In addition to pure mathematics, he did experimental work studying spectral lines of various elements (together with Heinrich Kayser), and was very interested in the application of this work to astronomical spectroscopy. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Traité de mécanique céleste, ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian probability, Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplace operator, Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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