Numerical investigation of all possible equilibria of dual spin satellites

This paper is the continuation of a previous work [6] in which we have obtained the set of all possible equilibria of a gyrostat satellite attracted by n points mass by solving two algebraical equations P₁=0 and P₂=0. It results that there is a maximum of 24 isolated equilibrium orientations for the satellite. Sufficient conditions of stability for these relative equilibria are given.Here we consider only the elementary case n=1. We show that the coefficients of the two algebrical equations depend on four parameters j₁, j₃, K and v². The two first parameters depend only on the direction of the internal angular momentum of the rotors, the third being only function of the principal moments of inertia of the satellite and the last parameter is a decreasing function of one of the components of . We show that the two polynomials P₁ and P₂ are unvariant within two transformations of the parameters j₁ and j₃. It is then possible to reduce the range of variation of these parameters.For some particular values of the parameters, it is possible to give the minimum number of real roots of equations P₁=0 and P₂=0. In general cases, a computing program is written to obtain the number of real roots of these equations according to the values of the parameters. We show that among the roots found, few of them corresponds to stable equilibrium orientations.     

A note on the correspondence between Mathieu's transformations and redundant variables in lagrangian mechanics

It is shown that, to any change of variables:q _i=q_i(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.

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Resumé On montre qu'à toute transformation:q _i=q_i(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.

     

Fracturation d'âge Aptien supérieur sur la bordure orientale de la plate-forme arabique (Haushi-Huqf,Oman)Aptian faulting (Shu'aiba Formation) on the eastern edge of the Arabian Platform (Haushi-Huqf,Oman)

In the Haushi-Huqf (Eastern Central Oman) as in other parts of the Arabian platform, a major sedimentary break is recorded between the Early Aptian carbonates (Shu'aiba Formation) and the Albian orbitolinid-rich marls (Nahr Umr Formation). The unconformity corresponds to a succession of events: (1) a brusque interruption of the regressive sequence of the Shu'aiba limestone (algae and small rudistid build-ups); (2) a stratigraphic gap related to the Late Aptian; (3) the development of a thick ferruginous crust (hardground) that covered the top surface of the Shu'aiba; the hardground is related to a forced flooding surface; (4) the Shu'aiba was rapidly drowned and buried under the Nahr Umr marls. Moreover, the Shu'aiba limestone was subject to faulting NW–SE-trending normal faults before lithification and formation of the ferruginous crust. The faulting episode is clearly dated: post-Early Aptian and pre-Albian. The signification of the faulting remains hypothetical. The syndiagenetic NW–SE normal faults may correspond to ‘en echelon’ faults, combined with transcurrent fault movements (for example the Haushi-Nafun Fault). The possible causes of these intra-platform transcurrent movements are discussed. To cite this article: C. Montenat, P. Barrier, C. R. Geoscience 334 (2002) 781–787.     

Measurement of natural stresses in a Provence mine (Southern France)

Stress measurements were carried out in the Arc syncline using drifs in a lignite mine. Eleven sites were investigated using the flat jack and hydraulic fracturing (or stimulating) methods. Two stress states were found to coexist, one isotropic, the other highly anisotropic. The orientations of the principal stresses are not homogeneous and an orientation ranging from E-W to NE-SW predominates locally. This does not accord with the regional stress field. The vertical stresses are systematically underestimated.     

L'accident du Toulourenc : une limite tectonique entre la plate-forme provençale et le Bassin vocontien à l'Aptien–Albien (SE France)

The WNW–ESE trending Toulourenc Fault Zone (TFZ) is the western segment of the major Ventoux–Lure Fault Zone, which separates the Provençal platform from the Baronnies Vocontian Basin. The TFZ was subject to polyphased Mid-Cretaceous movements, during the Early Aptian and Middle–Late Albian times. The latter faulting episode generated conglomerates and olistoliths resulting from dismantled faultscarps cutting Barremian–Bedoulian limestones. The deformation is related to compressional wrench faulting (NE–SW sinistral faults; dextral component for the TFZ). It induced the uplift of the northwestern corner of the platform, as indicated by a mid-Cretaceous hiatus (Early Aptian pro parte to Early Albian) narrowly delimited in space. The opening of submeridian grabens within the platform favoured the northward transit of channelised coarse-grained Albian sands originating from a southern area. To cite this article: C. Montenat et al., C. R. Geoscience 336 (2004).     

Further results from a laboratory model of the convective planetary boundary layer

The turbulence in a laboratory convective mixed layer is probed more extensively than in the preliminary study of Willis and Deardorff (1974), and results presented. Turbulence intensities, spectra and probability distributions using mixed-layer scaling compare favorably with similarly scaled field measurements not available or plentiful in 1974. However, the velocity spectra in the convection tank exhibit only a short inertial subrange due to the close proximity of the dissipation subrange to the energy-containing range.The turbulence budget suggests that the convergence of the vertical transport of pressure fluctuations is a rather important term.Results on the entrainment rate are also presented, using both mixed-layer scaling and local interfacial scaling.     

Definition of the Spatial Propagator and Implications for Magnetic Field Properties

Solar Physics - We study a quiet-Sun blowout jet which was observed on 2014 May 16 by the instruments on board the Solar Dynamics Observatory (SDO). We find the twin CME as jet-like and bubble-like...     

Trophic significance of the kelp Laminaria digitata (Lamour.) for the associated food web: a between-sites comparison

This study aimed at establishing the trophic significance of the kelp Laminaria digitata for consumers inhabiting two rocky shores of Northern Brittany (France), displaying contrasted ecological conditions. The general trophic structure did not vary between these two sites, with a wide diversity of filter-feeders and predators, and only 14% of the species sampled belonging to the grazers' trophic group. The diversity of food sources fueling the food web appeared also similar. The food webs comprised four trophic levels and the prevalence of omnivory appeared relatively low compared to previous studies in the same area. Conversely, to the food web structure, which did not differ, the biochemical composition of L. digitata differed between the two sites, and was correlated to a larger diversity of grazers feeding on this kelp in sheltered conditions. This indicated that the spatial variability occurring in the nutritive value of L. digitata is likely to deeply affect the functioning of kelp-associated food webs. The contribution of L. digitata-derived organic matter to the diet of filter-feeders inhabiting these two environments was assessed using the mixing model Isosource, which showed the higher contribution of kelp matter in sheltered conditions. These results highlight the spatial variability that may occur in the functioning of kelp-associated food webs. Moreover, this suggests that hydrodynamics is likely to control the availability of kelp-derived organic matter to local filter-feeders, probably through an increase of detritus export in exposed areas.