We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called PadenPanja controller [20] where unavailable generalized velocities are replaced by approximate differentiation ...

We show that there are ordinary differential equations in R with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.

We shall prove the existence of minimizers of the following functional f(u) = R T 0 L(x, u(x), u ′(x)) dx without convexity assumption. As a consequence of this result and the duality described in [10] we derive the existence of solutions for the Dirichlet problem for a certain differential inclusion being a generalization of the Euler–Lagrange equation of the functional f .

can be found in closed form by means of certain transformations on generating functions and the extraction of coefficients (see the end of section 3) suggested by Ira Gessel, and they comment: “He [Gessel] attributes this elegant technique, the ‘method of coefficients,’ to G. P. Egorychev.” Actually, in his book Integral Representation and Computation of Combinatorial Sums, Egorychev [4] (see [...

In this paper, the analysis is focused on single-time optimal control problems based on simple integral cost functionals from Lagrangians whose order is smaller than the higher order of ODEs constraints. The basic topics of our theory include: variational differential systems, adjoint differential systems, Legendrian duality, single-time maximum principle. The main original results refer to the...

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields ...

Pultruded composite structural members with open or closed thin-walled sections are being extensively used as columns for structural applications l1Jhere buckling is the main consideration in the design. In this paper, global buckling is investigated and critical loads are experimentally determined for various fiber reinforced composite I-beams of long column length. Southwell's method is used ...

Using an approach of modified Euler-Lagrange field equations obtained from an invariant action under infinitesimal modified general coordinates, local Lorentz and U∗(1) gauge transformations together with the corresponding Seiberg-Witten maps of the dynamical fields, a generalized Dirac equation in the presence of a constant electric field and a noncommutative cosmological anisotropic Bianchi I...

A kinematical study is made on the relation between the spin-singlet and spin-triplet pair distribution functions in the many-body system of spin-1/2 particles, and a group of inequalities is derived from the positiveness of the square of the "local spin" which is the total spin of a subsystem confined in a certain local region. This spin condition is applied to the neutron matter in the two-bo...

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions calculus variations and optimal control. Motivated this fact, we construct new, right-weighted generalized fractional derivative Riemann-Liouville sense with its associated integral for recently introduced weighted Mittag-Leffler kernel. We rewrite these operators equiva...