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. → *inner*; → *Lagrangian points*. |

لاگرانژی lâgrânži
*Fr.: 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 equation*s
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 equation*s and applied his mathematical techniques
to problems of → *mechanics*, especially those arising in astronomy. |

چگالی ِ لاگرانژی cagâli-ye Lagranži
*Fr.: densité lagrangienne*
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} d^{3}*V*.
Lagrangian density is often called Lagrangian when there is no ambiguity. → *Lagrangian*; → *density*. |

توانیک ِ لاگرانژی tavânik-e lâgrânži
*Fr.: 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*. |

دیسهگرایی ِ لاگرانژ disegerâyi-ye Lâgranži
*Fr.: 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*. |

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*. |

روش ِ لاگرانژی raveš-e Lâgrânži
*Fr.: 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*. |

بستاگر ِ لاگرانژ bastâgar-e Lagrange
*Fr.: 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 point*; → *multiplier*. |

ذرهی ِ لاگرانژی zarre-ye Lâgrânži
*Fr.: 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*. |

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*. |