Related papers: A Novel Variational Principle arising from Electro…

Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress…

We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket…

A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations…

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

Exceptional points are the branch-point singularities of non-Hermitian Hamiltonians, and have rich consequences in open-system dynamics. While the exceptional points and their critical phenomena are widely studied in the non-Hermitian…

Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…

The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including…

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…

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…

The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…

In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…

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…

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with…

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…