Lagrangian density

Lagrangian density

[lə′grän·jē·ən ′den· səd·ē]
(mechanics)
For a dynamical system of fields or continuous media, a function of the fields, of their time and space derivatives, and the coordinates and time, whose integral over space is the Lagrangian.
References in periodicals archive ?
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.
Such a form allows to maintain the original Einstein Lagrangian density as
There are two distinct definitions of a T-tensor from a Lagrangian: (i) the so-called "canonical" or "Noether" tensor, say [tau], is a byproduct of the Euler-Lagrange equations and (ii) the "Hilbert tensor," say T, is the symmetric tensor obtained as the derivative of the Lagrangian density with respect to variations of the (space-time) metric.
In the present work, we propose another hierarchy of generalized KdV equations based on modifying the Lagrangian density whose induced action functional is extremized by the KdV equation.
However, it should be especially stressed here that expression (A2) for the Lagrangian density makes sense only for spatial regions free of charged particles, which may include both EM radiation and bound EM field.
A Lagrangian density per unit volume of the reference configuration is introduced in [1-4,7,8,13]
The Lagrangian density of the (1 + 1) dimensional Chern-Simons-Higgs system is given by
Using the phase velocity (6) and adding the interaction terms with the gauge field, we can identify the full Lagrangian density as
The lagrangian density must distinguish electrons and positron by their charge only.
Consider the Dirac-limiting lagrangian density we can choose using only the complex valued [psi], [phi] and [[gamma].
A true unified field theory must not start with an arbitrarily concocted Lagrangian density (with merely the appearance of the metric determinant [square root of -g] together with a sum of variables inserted by hand), for this is merely a way to embed --and not construct from first principles--a variational density in an ad hoc given space (manifold).
In addition, we clearly see that [zeta] represents the lagrangian density characterizing the background field, thus lending support to our initial hypothesis regarding the lagrangian [XI].