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 ?
On one hand one must obtain the full low energy Lagrangians resulting from compactifications from ten to four dimensions.
He covers some variational problems in Hilbert spaces, iterative methods in Hilbert spaces, operator-splitting and alternating directions methods, augmented Lagrangians and alternating direct methods of multipliers, the least-squares solution of linear and nonlinear problems, obstacle problems and Bingham flow with applications to control, nonlinear eigenvalue problems, Eikonal equations, and fully nonlinear elliptic equations.
Classical lagrangians were varied in a formal manner with "second quantized" operators in approaches by Schwinger and Tomanaga and systematic procedures to handle the divergent terms were introduced [15,17].
Once you get through Lagrangians, Hamiltonians and Poisson brackets, you'll just have to grasp gauge symmetries and vector potentials.
n-harmonic mappings between annuli; the art of integrating free Lagrangians.
They fully describe infinite dimensional analysis, proper discretation, and the relationship between the two as they explain the existence of Lagrange multipliers, sensitivity analysis techniques, including Lipschitz continuity, first order augmented Lagrangians for equality and finite rank inequality constraints, augmented Lagrangian methods for non-smooth or convex optimization, Newton and sequential quadratic programming (SQP) methods, augmented Lagrangian-SQP methods, the primal-dual active set method, semismooth Newton methods, including applications, parabolic variational inequalities, and shape optimization.
Pons [6] has shown how to give a Hamiltonian formulation for higher order singular Lagrangians.
multiplication loops of locally compact topological translation planes; Lie groups which are the groups topologically generated by all left and right translations of topological loops; the inverse problem of the calculus of variations for second order ordinary differential equations: existence of variational multipliers, in particular, of multipliers satisfying the Finsler homogeneity conditions, and Riemannian and Finsler metrizability; metric structures associated with Lagrangians and Finsler functions variational structures in Finsler geometry and applications in physics (general relativity, Feynmam integral); Hamiltonian structures for homogeneous Lagrangians.
He covers Tonelli Lagrangians and Hamiltonians on compact manifolds, from KAM theory to Aubry-Mather theory, action-minimizing invariant measures for Tonelli Lagrangians, action-minimizing curves for Tonelli Lagrangians, and the Hamtonian-Jacobi equation and weak KAM theory.
We will show that, by making some rather formal changes in traditional lagrangians, some great simplifications can result.
More precisely, it is an extremal for all the least squares Lagrangians (depending on the Riemannian structure g)
They--particularly Neagu--present a Riemann-Lagrange geometry of 1-jet spaces that is suitable for the geometric study of the relativistic time-dependent Lagrangians.