Look up Lagrangian in Wiktionary, the free dictionary. Lagrangian may refer to: Lagrangian function, used to solve constrained minimization problems in...
1 KB (212 words) - 06:25, 28 October 2023
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least...
90 KB (14,229 words) - 07:47, 28 July 2024
Lagrange multiplier (redirect from Lagrangian multiplier)
reformulation of the original problem, known as the Lagrangian function or Lagrangian. In the general case, the Lagrangian is defined as L ( x , λ ) ≡ f ( x ) + ⟨...
50 KB (7,780 words) - 03:10, 29 July 2024
Symplectic manifold (redirect from Lagrangian submanifold)
\Omega _{2}} imaginary. A Lagrangian submanifold L {\displaystyle L} is called special if in addition to the above Lagrangian condition the restriction...
23 KB (3,630 words) - 10:43, 12 February 2024
Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used...
35 KB (5,951 words) - 16:28, 19 June 2024
In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual...
7 KB (854 words) - 03:42, 19 January 2024
In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization...
9 KB (1,098 words) - 01:50, 29 December 2023
In mathematics, a Lagrangian foliation or polarization is a foliation of a symplectic manifold, whose leaves are Lagrangian submanifolds. It is one of...
627 bytes (54 words) - 16:45, 6 February 2022
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods...
15 KB (1,934 words) - 13:22, 4 January 2024
In experimental fluid mechanics, Lagrangian Particle Tracking refers to the process of determining trajectories of small neutrally buoyant particles (flow...
2 KB (226 words) - 02:23, 8 August 2022
Lagrange point (redirect from Lagrangian Point)
In celestial mechanics, the Lagrange points (/ləˈɡrɑːndʒ/; also Lagrangian points or libration points) are points of equilibrium for small-mass objects...
50 KB (5,703 words) - 04:44, 18 July 2024
In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is 1/2n(n...
5 KB (713 words) - 23:31, 18 January 2023
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian...
52 KB (9,275 words) - 06:08, 11 July 2024
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations...
47 KB (6,757 words) - 00:00, 10 April 2024
1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle...
65 KB (10,847 words) - 16:13, 26 July 2024
Lagrangian analysis is the use of Lagrangian coordinates to analyze various problems in continuum mechanics. Lagrangian analysis may be used to analyze...
1,017 bytes (128 words) - 19:32, 4 July 2017
In mathematics, a Lagrangian system is a pair (Y, L), consisting of a smooth fiber bundle Y → X and a Lagrangian density L, which yields the Euler–Lagrange...
6 KB (757 words) - 06:51, 10 May 2024
relativistic Lagrangian mechanics is Lagrangian mechanics applied in the context of special relativity and general relativity. The relativistic Lagrangian can...
36 KB (5,560 words) - 02:18, 29 June 2024
List of objects at Lagrange points (redirect from List of objects at the Sun-Earth Lagrangian points)
Observatory exhausted its supply of liquid helium and was moved from the Lagrangian point in June 2013. 2009 – 2013: At the end of its mission ESA's Planck...
37 KB (2,531 words) - 07:45, 29 July 2024
Lagrange polynomial (redirect from Lagrangian interpolation)
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data...
22 KB (3,990 words) - 01:00, 13 April 2024
Trojan (celestial body) (redirect from Lagrangian asteroid)
orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points L4 and L5. Trojans can share the orbits of planets or of large...
14 KB (1,445 words) - 22:55, 18 July 2024
Hamiltonian optics (redirect from Lagrangian optics)
Lagrangian optics are two formulations of geometrical optics which share much of the mathematical formalism with Hamiltonian mechanics and Lagrangian...
34 KB (6,580 words) - 16:57, 23 September 2023
Duality (optimization) (redirect from Lagrangian duality)
the Lagrangian dual problem but other dual problems are used – for example, the Wolfe dual problem and the Fenchel dual problem. The Lagrangian dual...
27 KB (3,869 words) - 02:21, 15 April 2024
Dirac equation (redirect from Dirac Lagrangian)
The final step needed to write down a gauge-invariant Lagrangian is to add a Maxwell Lagrangian term, S Maxwell = ∫ d 4 x [ − 1 4 F μ ν F μ ν ] . {\displaystyle...
78 KB (12,971 words) - 00:26, 16 July 2024
Symplectic vector space (redirect from Lagrangian subspace)
that give such an isomorphism are called Lagrangian subspaces or simply Lagrangians. Explicitly, given a Lagrangian subspace as defined below, then a choice...
15 KB (2,275 words) - 13:33, 28 July 2024
In field theory, a nonlocal Lagrangian is a Lagrangian, a type of functional L [ ϕ ( x ) ] {\displaystyle {\mathcal {L}}[\phi (x)]} containing terms that...
2 KB (339 words) - 04:24, 12 February 2024
Classical mechanics (section Lagrangian mechanics)
others, leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics). These advances, made predominantly...
52 KB (5,826 words) - 19:21, 18 April 2024
The Semi-Lagrangian scheme (SLS) is a numerical method that is widely used in numerical weather prediction models for the integration of the equations...
4 KB (530 words) - 15:18, 8 August 2018
Einstein–Hilbert action (redirect from Einstein-Hilbert Lagrangian)
here for details). When a cosmological constant Λ is included in the Lagrangian, the action: S = ∫ [ 1 2 κ ( R − 2 Λ ) + L M ] − g d 4 x {\displaystyle...
15 KB (2,645 words) - 17:20, 21 June 2024
Newton's laws of motion (section Lagrangian)
that the Lagrangian formulation makes the conceptual content of classical mechanics more clear than starting with Newton's laws. Lagrangian mechanics...
121 KB (15,341 words) - 03:14, 27 July 2024