In this paper an exact model for a basic rst order -modulator is derived by means of a di erence equation. Furthermore, the second order di erence equation describing a second order -modulator is given. In addition, the conditions under which by using the exact rst order model this second order di erence equation is getting a simpler form is given too.

An effective action is obtained for the area and mass aspect of a thin shell of radiating selfgravitating matter. On following a mini-superspace approach, the geometry of the embedding space-time is not dynamical but fixed to be either Minkowski or Schwarzschild inside the shell and Vaidya in the external space filled with radiation. The Euler-Lagrange equations of motion are discussed and show...

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inpu...

We investigate essential spectrum of the Euler equation linearized about an arbitrary smooth steady flow in dimension 3. It is proved that for every Lyapunov-Oseledets exponent μ of the associated bicharacteristic-amplitude system, the circle of radius e has a common point with the spectrum. If, in addition, μ is attained on an aperiodic point, then the spectrum contains the entire circle.

In a paper of Klazar, several counting examples for rooted plane trees were given, including matchings and maximal matchings. Apart from asymptotical analysis, it was shown how to obtain exact formulas for some of the countings by means of the Lagrange inversion formula. In this note, the results of Klazar are extended to formulas for matchings, maximal matchings and maximum matchings for three...

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann–Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of the theorems of Green and Gauss, fractional Euler–Lagrange equations, and fractional natural boundary conditions. As an application we discuss...

A coupled Euler–Lagrange solution approach is used to model blast loading on a buried structure. The coupling algorithm is discussed along with a benchmark calculation.

We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Γ-converge to a continuum action functional acting on probability measures of particle trajectories. Also, the convergence of stationary points of the action is established. Minimizers of the limiting functional and, more generally, limiting distributions of s...

This paper presents a methodology to obtain transitional objects’ shapes by a physics-based simulation. Given two 2D/3D images of different objects or of the same object at different instants, using the Finite Element Method two models are built, and the Lagrange’s equation is solved to simulate the involved deformation. We used and compared two different finite elements to build each objects’ ...

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.