Lagrangian


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Lagrangian

[lə′grän·jē·ən]
(mechanics)
The difference between the kinetic energy and the potential energy of a system of particles, expressed as a function of generalized coordinates and velocities from which Lagrange's equations can be derived. Also known as kinetic potential; Lagrange function.
For a dynamical system of fields, a function which plays the same role as the Lagrangian of a system of particles; its integral over a time interval is a maximum or a minimum with respect to infinitesimal variations of the fields, provided the initial and final fields are held fixed.
References in periodicals archive ?
The essence of this approach is to replace the standard Eulerian density-like variables for cloud and precipitation fields with a probabilistic Lagrangian approach that applies point particles to represent the formation, growth, and fallout of cloud droplets, raindrops, and ice particles.
The stability of the Lagrangian points make them prime candidates for building up future space based resources.
The Lagrangian force density F comprises two parts of tension-compression [F.sub.S] and bending [F.sub.b] forces, i.e.
In this paper, we propose an alternative approach for the map from the canonical Lagrangian variables to the Eulerian variables.
Then in this case we use the Lagrangian derivative; for this we build the transported [bar.u]([theta]) on [[OMEGA].sub.0].
(ii) The subring of A* (X) containing divisors, Chern classes and Lagrangian constant cycle subvarieties injects into cohomology.
ABSTRACT: We reformulated the Lagrangian density for single fluid by using Caputo's fractional derivative, then from the fractional Euler-Lagrangian equation we obtained the equations that described the motion of single fluid in fractional form.
On the other hand, the choice N(t) = 1 for the gauge field on the Lagrangian formulation represents no difficulty; however, if we want to implement the Hamiltonian formulation of the theory and thus the quantum formulation, we have to keep the gauge arbitrary.
Similar to GPS, a high-precision satellite navigation constellation which consists of libration point satellites in the Earth-Moon system is introduced to provide navigation information for deep space probes, which can be called, accordingly, the Lagrangian point satellite navigation system.
The numerical computational model developed in this work for the transport of the particles is governed by the Lagrangian approach, where the particles are located following a concentration exponential law or randomly located in the space.
The FE simulation employed a Coupled Eulerian Lagrangian (CEL) technique.

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