Attitude equilibria of dual spin satellites subject to gravitational torques ofn bodies

We consider the motion of a dual spin satellite placed in the gravitational field of n material points, assuming that the satellite has no influence on the motion of these points. The main bodies are located at the libration points of the classical n bodies problem. We investigate the set of relative equilibria of the satellite. As in the elementary case of a gyrostat attracted by a single point, we show that this problem is equivalent to find the extremum of a quadratic function. We obtain all possible equilibria of the satellite by solving two algebraic equations. Sufficient conditions of stability of these relative equilibria are given.     

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.

     

An asymptotic solution for the stellar case of the planar Three-Body Problem

A simplified model of the planar Three-Body Problem is considered in which two particles, forming a close binary, orbit a distant point. A small parameter , related to the distance separating the binary and the remaining mass is defined. The time is eliminated from the equations of motion and an angular variable is used instead. A two-variable expansion procedure is used to find an asymptotic solution. The solution obtained is known completely up to the order ten in , and it is valid for almost arbitrary initial conditions. Specification of the initial conditions leads to a solution which is periodic with respect to a modified time variable.

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Résumé On considère un modèle simplifé du Problème Plan des Trois Corps, dans lequel deux particules, formant une binaire proche, sont en orbite par rapport à un troisième point éloigné des deux autres. On définit un petit paramètre , lié à la distance séparant la binaire de la particule restante. On élimine le temps des équations du mouvement et on utilise une variable angulaire comme nouvelle variable indépendante. Une méthode de développement à deux échelles est utilisée permettant d'obtenir une solution asymptotique du problème. La solution obtenue est connue complètement jusqu'àl'ordre dix en , et elle est valable pour des conditions initiales très générales. Pour des conditions initiales bien déterminées, on obtient une solution périodique par rapport à une nouvelle variable temporelle.

     

A reassessment of models for hydrocarbon generation in the Khibiny nepheline syenite complex, Kola Peninsula, Russia

Although hydrocarbon-bearing fluids have been known from the alkaline igneous rocks of the Khibiny intrusion for many years, their origin remains enigmatic. A recently proposed model of post-magmatic hydrocarbon (HC) generation through Fischer-Tropsch (FT) type reactions suggests the hydration of Fe-bearing phases and release of H₂ which reacts with magmatically derived CO₂ to form CH₄ and higher HCs. However, new petrographic, microthermometric, laser Raman, bulk gas and isotope data are presented and discussed in the context of previously published work in order to reassess models of HC generation. The gas phase is dominated by CH₄ with only minor proportions of higher hydrocarbons. No remnants of the proposed primary CO₂-rich fluid are found in the complex. The majority of the fluid inclusions are of secondary nature and trapped in healed microfractures. This indicates a high fluid flux after magma crystallisation. Entrapment conditions for fluid inclusions are 450–550 °C at 2.8–4.5 kbar. These temperatures are too high for hydrocarbon gas generation through the FT reaction. Chemical analyses of rims of Fe-rich phases suggest that they are not the result of alteration but instead represent changes in magma composition during crystallisation. Furthermore, there is no clear relationship between the presence of Fe-rich minerals and the abundance of fluid inclusion planes (FIPs) as reported elsewhere. δ¹³C values for methane range from − 22.4‰ to − 5.4‰, confirming a largely abiogenic origin for the gas. The presence of primary CH₄-dominated fluid inclusions and melt inclusions, which contain a methane-rich gas phase, indicates a magmatic origin of the HCs. An increase in methane content, together with a decrease in δ¹³C isotope values towards the intrusion margin suggests that magmatically derived abiogenic hydrocarbons may have mixed with biogenic hydrocarbons derived from the surrounding country rocks.     

The Dynamics of Small Postglacial Lake Basins and the Nature of Their Archaeological Record: A Case Study of the Middle Palaeolithic Site Neumark‐Nord 2, Germany

Due to favorable conditions of preservation, sedimentary basins provide rich records of human behavior and its environmental context. The conditions for the preservation of archaeological material however vary between basin types (large, river‐fed or small, closed basins), while conditions also differ within a particular basin environment. The goal of this paper is to understand how the dynamics of a small postglacial basin such as Neumark‐Nord 2, a context that dominates the Eemian archaeological record, affected the archaeology situated at its basin margin. The approach used here is to correlate the archaeological record with reconstructions of patterns of deposition and the water conditions within the basin, using lithology, micromorphology, pollen, and macroremains from a transect running from the basin center to the margin. The results show that (1) find levels were exposed to overland flow‐induced winnowing, which vertically concentrated finds but did not cause significant transport, (2) find levels correspond to phases of increased water presence in the basin, and (3) lateral shifts in hominin activity areas may reflect adjustments in the water level. The research shows the importance of large‐scale archaeological excavations and a multidisciplinary sampling strategy that covers both the basin center and the margins, when studying postglacial basin localities like Neumark‐Nord 2.     

MedFlux: Investigations of particle flux in the Twilight Zone

The MedFlux project was devised to determine and model relationships between organic matter and mineral ballasts of sinking particulate matter in the ocean. Specifically we investigated the ballast ratio hypothesis, tested various commonly used sampling and modeling techniques, and developed new technologies that would allow better characterization of particle biogeochemistry. Here we describe the rationale for the project, the biogeochemical provenance of the DYFAMED site, the international support structure, and highlights from the papers published here. Additional MedFlux papers can be accessed at the MedFlux web site (http://msrc.sunysb.edu/MedFlux/).