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We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…
This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
We apply Lie symmetry analysis of partial differential equations (PDEs) to the Euler-Lagrange equations of the two-Higgs-doublet model (2HDM), to determine its scalar Lie point symmetries. A Lie point symmetry is a structure-preserving…
In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary…
We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of…
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the…
The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic…
In this second part of the paper, we consider finite difference Lagrangians which are invariant under linear and projective actions of $SL(2)$, and the linear equi-affine action which preserves area in the plane. We first find the…
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle? To address this question, we develop a…
We consider the calculation of Euler--Lagrange systems of ordinary difference equations, including the difference Noether's Theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the…
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that in…
The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
General structure of classical reparametrization-invariant matter systems, mainly the relativistic particle and its $d$-brane generalization, are studied. The exposition is in close analogy with the relativistic particle in an…