# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 10 Search : Lagrangian
 inner Lagrangian point   نقطه‌ی ِ لاگرانژ ِ درونی   noqte-ye Lagrange-e daruni (#)Fr.: point de Lagrange interne   One of the five → Lagrangian points, denoted L1, which lies between the two bodies on the line passing through their center of mass. In a → close binary star system mass transfer occurs through this point. Lagrangian   لاگرانژی   lâgrânžiFr.: lagrangien   1) Of or relating to Joseph-Louis Lagrange (1736-1813), see below. 2) Same as → Lagrangian function. The Lagrangian of a → dynamical system describes its → dynamics and when subjected to an → action gives rise to → field equations and a → conservation law for the theory. Lagrangians are the keys for the mathematical formulation of field theories ( → field theory). See also: → inner Lagrangian point, → Lagrangian density, → Lagrangian dynamics, → Lagrangian formalism, → Lagrangian function, → Lagrangian method, → Lagrangian multiplier, → Lagrangian particle, → Lagrangian point.After the French/Italian mathematician Joseph-Louis Lagrange (1736-1813), who was the creator of the → calculus of variations (at the age of nineteen). He made also great advances in the treatment of → differential equations and applied his mathematical techniques to problems of → mechanics, especially those arising in astronomy. Lagrangian density   چگالی ِ لاگرانژی   cagâli-ye LagranžiFr.: densité lagrangienne   A quantity, denoted Ld, describing a continuous system in the → Lagrangian formalism, and defined as the → Lagrangian per unit volume. It is related to the Lagrangian L by: L = ∫∫∫Ld d3V. Lagrangian density is often called Lagrangian when there is no ambiguity.→ Lagrangian; → density. Lagrangian dynamics   توانیک ِ لاگرانژی   tavânik-e lâgrânžiFr.: dynamique lagrangienne   A reformulation of → Newtonian mechanics in which dynamical properties of the system are described in terms of generalized variables. In this approach the → generalized coordinates and → generalized velocities are treated as independent variables. Indeed applying Newton's laws to complicated problems can become a difficult task, especially if a description of the motion is needed for systems that either move in a complicated manner, or other coordinates than → Cartesian coordinates are used, or even for systems that involve several objects. Lagrangian dynamics encompasses Newton dynamics, and moreover leads to the concept of the → Hamiltonian of the system and a process by means of which it can be calculated. The Hamiltonian is a cornerstone in the field of → quantum mechanics.→ Lagrangian; → dynamics. Lagrangian formalism   دیسه‌گرایی ِ لاگرانژ   disegerâyi-ye LâgranžiFr.: formalisme lagrangien   A reformulation of classical mechanics that describes the evolution of a physical system using → variational principle The formalism does not require the concept of force, which is replaced by the → Lagrangian function. The formalism makes the description of systems more simpler. Moreover, the passage from classical description to quantum description becomes natural. Same as → Lagrangian dynamics.→ Lagrangian; → formalism. Lagrangian function   کریای ِ لاگرانژ   karyâ-ye lâgrânž (#)Fr.: Lagrangien, fonction de Lagrange   A physical quantity (denoted L), defined as the difference between the → kinetic energy (T) and the → potential energy (V) of a system: L = T - V. It is a function of → generalized coordinates, → generalized velocities, and time. Same as → Lagrangian, → kinetic potential.→ Lagrangian; → function. Lagrangian method   روش ِ لاگرانژی   raveš-e LâgrânžiFr.: méthode lagrangienne   Fluid mechanics: An approach in which a single fluid particle (→ Lagrangian particle) is followed during its motion. The physical properties of the particle, such as velocity, acceleration, and density are described at each point and at each instant. Compare with → Eulerian method.→ Lagrangian; → method. Lagrangian multiplier   بستاگر ِ لاگرانژ   bastâgar-e LagrangeFr.: multiplicateur de Lagrange   Math.: A constant that appears in the process for obtaining extrema of functions of several variables. Suppose that the function f(x,y) has to be maximized by choice of x and y subject to the constraint that g(x,y)≤ k. The solution can be found by constructing the → Lagrangian function  L(x,y,λ) = f(x,y) + λ[k - g(x,y)], where λ is the Lagrangian multiplier. Lagrangian particle   ذره‌ی ِ لاگرانژی   zarre-ye LâgrânžiFr.: particule lagrangienne   Fluid mechanics: In the → Lagrangian method, a particle that moves as though it is an element of fluid. The particle concept is an approach to solving complicated fluid dynamics problems by tracking a large number of particles representing the fluid. The particle may be thought of as the location of the center of mass of the fluid element with one or more property values.→ Lagrangian; → particle. Lagrangian point   نقطه‌های ِ لاگرانژ   noqtehâ-ye Lagrange (#)Fr.: points de Lagrange   On of the five locations in space where the → centrifugal force and the → gravitational force of two bodies (m orbiting M) neutralize each other. A third, less massive body, located at any one of these points, will be held in equilibrium with respect to the other two. Three of the points, L1, L2, and L3, lie on a line joining the centers of M and m. L1 lies between M and m, near to m, L2 lies beyond m, and L3 on the other side of M beyond the orbit. The other two points, L4 and L5, which are the most stable, lie on either side of this line, in the orbit of m around M, each of them making an equilateral triangle with M and m. L4 lies in the m's orbit approximately 60° ahead of it, while L5 lies in the m's orbit approximately 60° behind m. See also → Trojan asteroid; → Roche lobe; → equipotential surface; → horseshoe orbit.→ Lagrangian; → point.