Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a varia-tional principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial...

We study Hamiltonian stationary Lagrangian surfaces in C, i.e. Lagrangian surfaces in C which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representation and produce all tori through either the integrable systems machinery or more di...

We prove that for a uniformly convex Lagrangian system L on a compact manifold M , almost all energy levels contain a periodic orbit. We also prove that below Mañé’s critical value of the lift of the Lagrangian to the universal cover, cu(L), almost all energy levels have conjugate points. We prove that if the energy level [E = k] is of contact type and M 6= T then the free time action functiona...

The paper deals with the economic dispatch problem for a district heating system. The distribution network is modeled with a number of nodes and arcs, implying that time delays and restrictions in distribution capacity can be considered. A solution algorithm for the corresponding nonlinear optimization problem is proposed. The method is based on Lagrangian relaxation and exploits the relations ...

The moduli space dynamics of vortices in the Jackiw-Pi model where a non-relativistic Schrödinger field couples minimally to Chern-Simons gauge field, is considered. It is shown that the difficulties in direct application of Manton’s method to obtain a moduli-space metric in the first order system can be circumvented by turning the Lagrangian into a second order system. We obtain exact metrics ...

This thesis presents a study of five different Lagrangian heuristics applied to the strictly convex quadratic minimum cost network flow problem. Tests are conducted on randomly generated transportation networks with different degrees of sparsity and nonlinearity according to a system devised by Ohuchi and Kaji [18]. The different heuristics performance in time and quality are compared. The unco...

We present a method to study the time variation of the orbital parameters of a Post–Keplerian binary system undergoing a generic external perturbation. The method is the relativistic extension of the planetary Lagrangian equations. The theory only assumes the smallness of the external perturbation while relativistic effects are already included in the unperturbed problem. This is the major adva...

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some ...

The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems, observability and invariant differential forms. The approach is applicable to non-degenerate optimal control systems with smooth integral cost function. The cost functi...