|
Eulerian Coordinates
In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple yet ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them ''after'' Euler. Conjectures *Euler's sum of powers conjecture disproved for exponents 4 and 5 during the 20th century; unsolved for higher exponents * Euler's Graeco-Latin square conjecture proved to be true for and disproved otherwise, during the 20th century Equations Usually, '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler - Jakob Emanuel Handmann (Kunstmuseum Basel)
Leonhard is a male given name and surname in German and other Germanic languages, as well as Estonian language, Estonian, sharing the same origin as English Leonard. Notable people with the name include: Given name *Alfred Leonhard Maluma (1955–2021), Tanzanian Roman Catholic prelate *Alfred Leonhard Tietz (1883–1941), German entrepreneur *Anton Leonhard Franzen (1896–1968), German lawyer and Nazi politician *Arne Leonhard Nilsen (1893–1957), Norwegian politician *Artur Leonhard Kasterpalu (1897–1942), Estonian politician *Benedikt Maria Leonhard von Werkmeister (1745–1823), German Roman Catholic theologian *Diederich Franz Leonhard von Schlechtendal (1794–1866), German botanist *Dieterich Leonhard Oskamp (1756–1803), Dutch natural historian and author *Friedrich Georg Leonhard Miedke (1803–1842), German actor, singer, composer, theatre director, painter and author *Fritz Leonhard Redlich (1892–1978) was a German businessman and economic historian *Hans Leonhard S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Body
In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. Mechanics of rigid bodies is a field within mechanics where motions and forces of objects are studied without considering effects that can cause deformation (as opposed to mechanics of materials, where deformable objects are considered). In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light, where the mass is infinitely large. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Poisson–Darboux Equation
In mathematics, the Euler–Poisson–Darboux(EPD) equation is the partial differential equation : u_+\frac=0. This equation is named for Siméon Poisson, Leonhard Euler, and Gaston Darboux. It plays an important role in solving the classical wave equation. This equation is related to : u_+\fracu_r-u_=0, by x=r+t , y=r-t , where N=\frac and some sources quote this equation when referring to the Euler–Poisson–Darboux equation. The EPD equation equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, therefore it has an interest as a paradigm to relativity theory. Compact support self-similar solution of the EPD equation for thermal conduction was derived starting from the modified Fourier-Cattaneo law. It is also possible to solve the non-linear EPD equations with the method of generalized separation of variables In mathematics, separation of variables (also known as the Fourier method) is any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Tricomi Equation
In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named after mathematicians Leonhard Euler and Francesco Giacomo Tricomi. : u_+xu_=0. \, It is elliptic in the half plane ''x'' > 0, parabolic at ''x'' = 0 and hyperbolic in the half plane ''x'' < 0. Its characteristics are : which have the integral : where ''C'' is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line ''x'' = 0, the curves lying on the right hand side of the ''y''- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all. A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume. From Noether's theorem, every differe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inviscid Flow
In fluid dynamics, inviscid flow is the flow of an ''inviscid fluid'' which is a fluid with zero viscosity. The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, such as the case of inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler equation. This simplified equation is applicable to inviscid flow as well as flow with low viscosity and a Reynolds number much greater than one. Using the Euler equation, many fluid dynamics problems involving low viscosity are easily solved, however, the assumed negligible viscosity is no longer valid in the region of fluid near a solid boundary (the boundary layer) or, more generally in regions with large velocity gradients which are evidently accompanied by viscous forces. The flow of a superfluid is inviscid. Inviscid flows are broadly classified into potential flows (or, irrotational flows) and rotational inviscid flows. Prandtl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n - 1 derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation. In one spatial dimension, this is \frac = c^2 \frac The equation has the property that, if and its first time derivative are arbitrarily specified initial data on the line (with sufficient smoothness properties), then there exists a solution for all time . The solutions of hyperbolic equations are "wave-like". If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point of space feels the disturbance at once. Relative to a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Equations (fluid Dynamics)
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible and compressible flows. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is divergence-free. The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler. However, fluid dynamics literature often refers to the full set of the compressible Euler equations – including ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Differential Equation
In mathematics, Euler's differential equation is a first-order non-linear ordinary differential equation, named after Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential .... It is given by:Ince, E. L. "L. 1944 Ordinary Differential Equations." 227. :\frac + \frac = 0 This is a separable equation and the solution is given by the following integral equation: :\int \frac + \int \frac = c References Eponymous equations of physics Mathematical physics Ordinary differential equations Leonhard Euler {{math-physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinates
In mathematics, the polar coordinate system specifies a given point (mathematics), point in a plane (mathematics), plane by using a distance and an angle as its two coordinate system, coordinates. These are *the point's distance from a reference point called the ''pole'', and *the point's direction from the pole relative to the direction of the ''polar axis'', a ray (geometry), ray drawn from the pole. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. The pole is analogous to the origin in a Cartesian coordinate system. Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
