A general model of solids with vectorial microstructures is introduced. The field equationsare the obtained as Euler-Lagrange equations of a suitable energetic functional. The Cosserat model is encompassed in this model and it can be used to study the behaviour of granular media. A first approach to this problem deals with a two dimensional model, since in such a case the field equations have a...

We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.

A concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of a C 1 differential equation is considered. When the second compound of the variational equation with respect to this solution is uniformly asymptotically stable and the omega limit set contains no...

One of recent achievements in the field of nonlinear H∞ optimal control theories for Euler-Lagrange systems is the analytic solution to the Hamilton-JacobiIsaccs (HJI) equation associated to the so-called nonlinear H∞ inverse-optimal control [1]. In this paper, we address the problem of nonlinear H∞ optimal control design for an Euler-Lagrange system, rather than the inverse-optimal problem. By...

We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagra...

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy limdet ξ→0+ W (ξ) = ∞. We initiate a study which we hope would lead to a theory for the existence and uniqueness of minimizers of functionals of the form E(u) = ∫ Ω (W (∇u) − F · u)dx, as well as their Euler–Lagrange equations. The techniques dev...

The equations of motion of multibody systems with holonomic constraints are of index 3 and therefore not directly solvable by standard ODE or DAE methods. Until now, a number of regularization methods have been proposed to treat these systems [1, 2, 3, 4], but as they are based on different points of view they have never been compared with respect to their physical properties, invariance under ...

Using a differential geometric treatment, we analytically derived the expression for De Sitter geodesic precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild’s metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O’Connell 1970, 1975 in a different sett...

We prove the following results: (1) A unique smooth solution exists for short time for the heat equation associated with the MM obius energy of loops in a euclidean space, starting with any simple smooth loop. (2) A critical loop of the energy is smooth if it has cube-integrable curvature. Combining this with an earlier result of M. Freedman, Z. Wang and the author, any local minimizer of the e...