Displaying 1041 – 1060 of 1123

Showing per page

Une approche géométrique du contrôle optimal de l’arc atmosphérique de la navette spatiale

Bernard Bonnard, Emmanuel Trélat (2002)

ESAIM: Control, Optimisation and Calculus of Variations

L’objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l’arc atmosphérique optimal d’une navette spatiale (problème de rentrée sur Terre ou programme d’exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l’angle de gîte cinématique et le coût est l’intégrale du flux thermique. Par ailleurs il y a des contraintes sur l’état (flux thermique, accélération normale et pression dynamique). Notre étude...

Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale

Bernard Bonnard, Emmanuel Trélat (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this article is to make some geometric remarks and some preliminary calculations in order to construct the optimal atmospheric arc of a spatial shuttle (problem of reentry on Earth or Mars Sample Return project). The system describing the trajectories is in dimension 6, the control is the bank angle and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is mainly geometric and is founded on the...

Uses of new sensitivity and DAE solving methods in SmartMOBILE for verified analysis of mechanical systems

Ekaterina Auer, Wolfram Luther (2009)

International Journal of Applied Mathematics and Computer Science

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SmartMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities...

Using symbolic computation in the characterization of frictional instabilities involving orthotropic materials

Mohamed A. Agwa, António Pinto da Costa (2015)

International Journal of Applied Mathematics and Computer Science

The present work addresses the problem of determining under what conditions the impending slip state or the steady sliding of a linear elastic orthotropic layer or half space with respect to a rigid flat obstacle is dynamically unstable. In other words, we search the conditions for the occurrence of smooth exponentially growing dynamic solutions with perturbed initial conditions arbitrarily close to the steady sliding state, taking the system away from the equilibrium state or the steady sliding...

Variational calculus on Lie algebroids

Eduardo Martínez (2008)

ESAIM: Control, Optimisation and Calculus of Variations

It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

Variational formulations I: Statics of mechanical systems

Włodzimierz M. Tulczyjew (2011)

Communications in Mathematics

Two improvements of variational formulations of mechanics are proposed. The first consists in a modification of the definition of equilibrium. The second consists in adding elements of control by external devices. In the present note the proposed improvements are applied to variational principles of statics. Numerous examples are given.

Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset, Pedro D. Prieto-Martínez, Narciso Román-Roy (2016)

Communications in Mathematics

The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special...

Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents

Marcella Palese (2016)

Communications in Mathematics

We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local...

Currently displaying 1041 – 1060 of 1123