Wiktionary
a. (alternative case form of Lagrangian English) n. (alternative case form of Lagrangian English)
Wikipedia
Lagrangian may refer to:
- Lagrangian, relating to Joseph-Louis Lagrange (1736–1813), Italian mathematician and astronomer
Lagrangian field theory is a formalism in classical field theory. It is the field theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used for discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.
This article uses L for the Lagrangian density, and L for the Lagrangian.
The Lagrangian mechanics formalism was generalized further to handle field theory. In field theory, the independent variable is replaced by an event in spacetime (x, y, z, t), or more generally still by a point s on a manifold. The dependent variables (q) are replaced by the value of a field at that point in spacetime φ(x, y, z, t) so that the equations of motion are obtained by means of an action principle, written as:
$$\frac{\delta \mathcal{S}}{\delta \varphi_i} = 0,\,$$
where the action, S, is a functional of the dependent variables φ(s) with their derivatives and s itself
$$\mathcal{S}\left[\varphi_i\right] = \int{ \mathcal{L} \left(\varphi_i (s), \frac{\partial \varphi_i (s)}{\partial s^\alpha}, s^\alpha\right) \, \mathrm{d}^n s }$$
and where s = { s} denotes the set of n independent variables of the system, indexed by α = 1, 2, 3,..., n. Notice L is used in the case of one independent variable (t) and L is used in the case of multiple independent variables (usually four: x, y, z, t).
Usage examples of "lagrangian".
Several thruster clusters helped maintain its position at the unstable Lagrangian point.
Also it has not reached its final orbital location, which is the opposite Lagrangian point.
This bottle is located at the Lagrangian point 60 degrees ahead of Marn, so that about two-thirds of the planetary surface is lighted by the star.
More than a hundred ships spread in a rough sphere a thousand kilometers in diameter, in the Lagrangian point sixty degrees of arc ahead of Dione.
Farside Lagrangian point was not truly gravitationally stable, it was worth the fuel costs required to hold a communications station there to provide a relay point for the entire hemisphere.
Several satellites and habitats had already spiraled down to impacts on the Moon, including all of the satellites stationed at the Lagrangian balance points.
They would deliver it to one of the Lagrangian powerstats, collect their money, and hopefully, no one would be the wiser.
The directorate maintains it in the leading Earth--Sun Lagrangian point with the rest of the mothball fleet.
It had docked an hour after their arrival onboard the Quito Shuttle and boosted for the leading Earth-Sun Lagrangian point shortly thereafter.
The plot appears to be based in the Belt and aboard several of the Lagrangian Settlements.
For safety, only minimal quantities of reaction mass had been carried aboard since the journey from the Earth-Sun Lagrangian point.
Mars and was lodged at L1, the crucial Lagrangian point suspended between Earth and sun.
L-3 is on the opposite side of the Earth from the moon and is of no use to anybody, but L-1 and L-2, the quasi-stable Lagrangian points near the moon, are different.
Four, also known as Highgate, is an interplanetary shipping port located in a Lagrangian halo orbit near the Moon.
Approximate symmetries of Lagrangians give rise to approximate conservation laws.