Search results for " mechanics."
showing 10 items of 5002 documents
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
2007
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global opti…
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
2008
Abstract The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.
One-parameter family of Clairaut-Liouville metrics
2007
Riemannian metrics with singularities are considered on the $2$-sphere of revolution. The analysis of such singularities is motivated by examples stemming from mechanics and related to projections of higher dimensional (regular) sub-Riemannian distributions. An unfolding of the metrics in the form of an homotopy from the canonical metric on $\SS^2$ is defined which allows to analyze the singular case as a limit of standard Riemannian ones. A bifurcation of the conjugate locus for points on the singularity is finally exhibited.
A flux based conservation approach for acoustic problems
2008
International audience
Galerkin and control-volume FEMs evaluation for acoustic problems
2004
International audience
Analyse de la dispersion de la solution MVCEF pour l'équation de Helmholtz
2006
Investigation of the vibrational dynamics of the HCN/CNH isomers through high order canonical perturbation theory
2000
International audience; Molecular vibrations of the molecule HCN/CNH are examined using a combination of a minimum energy path Hamiltonian and high order canonical perturbation theory , as suggested in a recent work [D. Sugny and M. Joyeux, J. Chem. Phys. 112, 31 (2000)]. In addition, the quantum analog of the classical CPT is presented and results obtained therefrom are compared to the classical ones. The MEP Hamiltonian is shown to provide an accurate representation of the original potential energy surface and a convenient starting point for the CPT. The CPT results are subsequently used to elucidate the molecular dynamics: It appears that the isomerization dynamics of HCN/CNH is very tri…
Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups
2004
International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…
Implementation of single-qubit quantum gates by adiabatic passage and static laser phases
2006
International audience; We propose and analyse experimentally feasible implementations of single-qubit quantum gates based on stimulated Raman adiabatic passage (STIRAP) between magnetic sublevels in atoms coupled by elliptically polarized pulsed laser fields, in part based on a proposal by Kis and Renzoni [Z. Kis, F. Renzoni, Phys. Rev. A 65 (2002) 032318]. These techniques require only the control of the relative phase of the driving fields but do not involve any dynamical or geometric phases, which makes it independent of the other interaction details: detuning, pulse shapes, pulse areas and pulse durations. The suggested techniques are immune to spontaneous emission since the qubit mani…