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 define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler-Einstein metrics, and are automatically Kähler-Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existen...

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 .

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...

We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is supported on the intersection of a hyperplane with a level set of a function which is homogeneous of degree two. Moreover, we perform second variations to obtain t...

I have used a novel approach based upon Hamiltonian mechanics to derive new equations for nearly geostrophic motion in a shallow homogeneous fluid. The equations have the same order accuracy as (say) the quasigeostrophic equations, but they allow order-one variations in the depth and Coriolis parameter. My equations exactly conserve proper analogues of the energy and potential vorticity, and th...

In this paper, He’s variational iterative method has been applied to give exact solution of the Euler Lagrange equation which arises from the variational problems with moving boundaries and isoperimetric problems. In this method, general Lagrange multipliers are introduced to construct correction functional for the variational problems. The initial approximations can be freely chosen with possi...