Related papers: Variational principle for contact Tonelli Hamilton…

We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one…

We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be…

The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian…

We develop a variational method for interacting surface systems with higher-form global symmetries. As a natural extension of the conventional second-quantized Hamiltonian of interacting bosons, we explicitly construct a second-quantized…

We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…

In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of…

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…

The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…

Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…

This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their…

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…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.

Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…

Recently, Li, Li and Zhang introduced the topological pressure for correspondences and measure-theoretic entropy for transition probability kernels. Building thereon, they established a variational principle for correspondences satisfying…

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…