Related papers: On the Variational Characterisation of Generalized…
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…
The Lagrangian proposed by York et al. and the covariant first order Lagrangian for General Relativity are introduced to deal with the (vacuum) gravitational field on a reference background. The two Lagrangians are compared and we show that…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
We classify all the six derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six, reduces to an arbitrary linear…
The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
Generalized symmetries and supersymmetries depending on derivatives of dynamic variables are treated in a most general setting. Studding cohomology of the variational bicomplex, we state the first variational formula and conservation laws…
The recent progress in the study of Galileons, i.e. equations of second order with an action invariant under a Galilean transformation is related to work on `Universal Field Equations' \cite{dbfgov} which are second order equations arising…
Onsager and Machlup proposed a second order variational-principle in order to include inertial effects into the Langevin-equation, giving a Lagrangian with second order derivatives in time. This but violates Ostrogradysky's theorem, which…
This paper develops a structure-preserving numerical integration scheme for a class of higher-order mechanical systems. The dynamics of these systems are governed by invariant variational principles defined on higher-order tangent bundles…
We show how the homogeneous variational bicomplex provides a useful formalism for describing a number of properties of single-integral variational problems, and we introduce a subsequence of one of the rows of the bicomplex which is locally…
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…
As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…
Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincar\'e-Cartan form of which is…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
The gauge covariant derivative of a wave function is ubiquitous in gauge theory, and with associated gauge transformations it defines charged currents interacting with external fields, such as the Lorentz force exerted by an electromagnetic…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped…
In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…