An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

A set of second order → differential equations for a system of particles which relate the kinetic energy of the system to the → generalized coordinates, the generalized forces, and the time. If the motion of a → holonomic system is described by the generalized coordinates q₁, q₂, ..., q_n and the → generalized velocities  q^.₁, q^.₂, ..., q^._n, the equations of the motion are of the form: d/dt (∂T/∂q^._i) - ∂T/∂q^._i = Q_i (i = 1, 2, ..., n), where T is the kinetic energy of the system and Q_i the generalized force.

→ Lagrangian; → equation.

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.

A quantity, denoted L_d, 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 = ∫∫∫L_d d³V.
Lagrangian density is often called Lagrangian when there is no ambiguity.

→ Lagrangian; → density.

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.

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.

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.

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.

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 point; → multiplier.

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.

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.

A body of fresh or salt water entirely surrounded by land.

From O.Fr. lack, from L. lacus "pond, lake," related to lacuna "hole, pit," from PIE *lak- (cf. Gk. lakkos "pit, tank, pond," O.C.S. loky "pool, cistern," O.Ir. loch "lake, pond").

Daryâcé, from daryâ "sea" Mid.Pers. daryâp variant zrah; O.Pers. drayah-; Av. zrayah- "sea;" cf. Skt. jráyas- "expanse, space, flat surface" + -cé diminutive suffix, from Mid.Pers. -cak, variants -êžak (as in kanicak "little girl," sangcak "small stone," xôkcak "small pig"), also Mod.Pers. -ak.

A young sheep; the meat of a young sheep.

M.E., O.E.; cognate with Du. lam, Ger. Lamm, Goth. lamb; akin to Gk. elaphos "deer."

Mid.Pers. warrag "lamb; sheep;" warân "ram;" Av. varən-; cf. Skt. uaran-; L. vervex (Fr. brebis); Arm. garn; Baluci garând "ram;" Lori, Laki veran "ram;" PIE *wrhen- "lamb."

A tiny change in the → energy levels of the → hydrogen atom between the states 2S_1/2 and 2P_1/2, which creates a shift in the corresponding → spectral lines. The 2P_1/2 state is slightly lower than the 2S_1/2 state, contrarily to the Schrodinger's solution. The difference is explained by the interaction between → vacuum energy fluctuations and the hydrogen electron in different orbitals.

Named after Willis Eugene Lamb, Jr. (1913-2008), an American physicist who discovered this effect in 1951, and won the Nobel Prize in physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum;" → shift.

The eleventh letter of the Greek alphabet. In lower case, λ, it denotes → wavelength. It is also used in the → Bayer designation system to identify a specific star in a → constellation. See also → lambda point.
In upper case, Λ, it represents the → cosmological constant or → dark energy.

From Phoenician lamedh.

The prototype of a small class of stars (A-F types) which have weak metallic lines (indicating that they are depleted in metals heavier than Si, but with solar abundances of C, N, O, and S). Moreover, they have moderately large rotational velocities and small space velocities. Lambda Boo stars may be pre-main-sequence objects, or they may be main sequence stars that formed from gas whose metal atoms had been absorbed by interstellar dust.

Named after the prototype, the star → Lambda (λ) of constellation → Bootes; → star.

The → standard model of → Big Bang that incorporates both → dark matter and → dark energy. See also → cold dark matter (CDM).

→ lambda, → cosmological constant; → cold; → dark; → matter; → model.

Same as → Meissa.

Lambda (λ), a Greek letter used in the → Bayer designation of star names.

The temperature (roughly 2.17 K) at which → liquid helium (→ helium I) becomes → superfluid (→ helium II).

The name was given by the Dutch physicist Willem Hendrik Keesom (1876-1956), who discovered the behavior of helium near this transition point and successfully solidified helium in 1926 (under an external pressure of 25 atmospheres). The name was originally suggested by Paul Ehrenfest (1880-1933), who was inspired by the shape of the → specific heat curve, which resembles the Gk. letter → lambda; → point.

A centimeter-gram-second (cgs) unit of luminance (or brightness) equal to 1/π candle per square centimeter. Physically, the lambert is the luminance of a perfectly diffusing white surface receiving an illuminance of 1 lumen per square centimeter.

Johann Heinrich Lambert (1728-1777), German scientist and mathematician; → law.

The intensity of the light emanating in any given direction from a perfectly diffusing surface is proportional to the cosine of the angle between the direction and the normal to the surface. Also called → Lambert's law.

→ lambert; → cosine; → law.