Related papers: Variations in Discrete Mechanics and Field Theory
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
We consider the variational principle for the Lagrangian 1-form structure for long-range models of Calogero-Moser (CM) type. The multiform variational principle involves variations with respect to both the field variables as well as the…
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…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite…
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…
The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete…
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.…
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…
We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles).…
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…
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through…
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…