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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…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
Hamilton's principle does not formally apply to systems whose boundary conditions lie outside configuration space, but extensions are possible using certain "natural" boundary conditions that allow action extremization. With the single…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary.…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also {\it constraint equations}. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The…
We consider a class of Lagrangians that depend not only on some configurational variables and their first time derivatives, but also on second time derivatives, thereby leading to fourth-order evolution equations. The proposed higher-order…
We consider the compatibility of the equations of motion which follow from d'Alembert's principle in the case of a general autonomous non-holonomic mechanical system in N dimensions, with those equations which follow for the same system by…
A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…
In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this…