On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a non zero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term "quasi-satellite" more and more present in the literature. However, some authors rather use the term "retrograde satellite" when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.Comment: 30 pages, 13 figures, 1 tabl

The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L 3 , L 4 and L 5 emerging periodic orbits families and remarked that for very high eccentricities F L4 and F L5 merge with F L3 which bifurcates to a stable family

Die "Beckenkammspan-Interpositionsarthrodese" des oberen Sprunggelenks

Zusammenfassung: Operationsziel: Stabile und korrekt positionierte Arthrodese des oberen Sprunggelenks (OSG) zur Wiederherstellung einer schmerzfreien Belastbarkeit der Gliedmaße. Indikationen: Invalidisierende, schmerzhafte OSG-Arthrose mit umfangreichem Knochendefekt bei Status nach Trauma, Infekt oder bei schweren Deformitäten wie z. B. kongenitalen Fehlbildungen oder diabetischen Osteoarthropathien. Kontraindikationen: Akuter Gelenkinfekt. Schwere arterielle Verschlusskrankheit der betroffenen unteren Extremität. Operationstechnik: Lateraler Zugang zur distalen Fibula. Fibulaosteotomie 7 cm proximal der Fibulaspitze. Zurückklappen der distalen Fibula nach dorsal und Darstellen des OSG. Vollständige Entknorpelung der Gelenkflächen und Débridement des Knochendefekts. Bestimmung der Defektgröße. Entnahme eines entsprechenden trikortikalen Beckenkammspans. Entnahme von autogener Spongiosa am Beckenkamm oder an der proximalen lateralen Tibia. Einbringen der trikortikalen Späne und Ausfüllen des Defekts mit abstützender Wirkung. Fixation mit 6,5-mm- und 3,5-mm-Titan-AO-Zugschrauben. Je nach Ausdehnung des Defekts zusätzliche Stabilisierung des Spans mit einer Titanplatte. Laterale Stabilisierung durch direkte Verschraubung der distalen Fibula an Talus und Tibia. Schichtweiser Wundverschluss. Gespaltener Unterschenkelliegegipsverband in Neutralstellung des OSG. Weiterbehandlung: Erster Wechsel des Gipsverbands nach 48 h. Mobilisation im abnehmbaren Unterschenkelliegegipsverband mit Vollentlastung für 6 Wochen. Teilbelastung mit 15 kg für weitere 6 Wochen. Erste klinische und radiologische Verlaufskontrolle 6 Wochen postoperativ. Ergebnisse: Zwischen Januar 2002 und Januar 2004 wurden fünf Patienten (vier Frauen, ein Mann, Durchschnittsalter 57 Jahre [42-77 Jahre]) mit schweren Knochendefekten im OSG behandelt. Keine intra- oder frühen postoperativen Komplikationen. Der AOFAS-Score (American Orthopedic Foot and Ankle Society) konnte von 23 Punkten präoperativ auf 76 Punkte (Maximum 86 Punkte) postoperativ verbessert werden (Durchschnittsverlauf 25 Monate). Zwei Patienten entwickelten eine Pseudarthrose und mussten sich einer erneuten Operation mit einem Sprunggelenkarthrodesennagel unterziehen. Eine Valgusfehlstellung nach der Arthrodese wurde bei einer Patientin mit einer supramalleolären Korrekturosteotomie behandel

Let’s Make it Clear: The Integration of Plain Language into Technical Communication Coursework

Plain language is writing that is clear, concise, and audience focused. Plain language concepts help readers find their needed information quickly and allow them to understand it the first time they read it. Because technical communication shares many of the same goals of plain language, it is imperative that early coursework in technical communication and writing incorporate these concepts; however, this is often not the case. The goal of this project is to integrate plain language into the coursework of Technical Rhetoric & Genres, an English course for both technical communication students and outside majors alike. Through intensive research, material creation, and discussion-based class activities, I seek to form the connection between plain language and technical communications and emphasize the importance of utilizing these concepts to write the most accessible and clear work possible. Doing so reveals that students across all disciplines benefit from these lessons and are able to create connections to their coursework within the class, as well as understand the interdisciplinary application of plain language across all genres and contexts as they move into future coursework and professional writing environments

Des "mauvaises langues" dans Richard III

International audienceEmprunté à A Treatise of The Good and Eveil Toungue, traduction du Traité de la bonne et mauvaise langue de Jean de Marconville,2 dont l'un des mots d'ordre est "rule thy tongue,"3 ce passage résume bien ce qu'est la "politique de la langue" à l'époque élisabéthaine. Quand on étudie les homélies et les sermons, tels que "An Homélie agaynst Contention and Braulynge,"4 ou "The Taming of the Tongue,"5 qui condamnent l'insulte sous toutes ses formes, qu'elle soit insulte à Dieu ("swearing," "blasphemy"), aux hommes ("railing," "scoffing," "back -biting," "slandering"), ou aux deux ("cursing," "banning"), quand on explore des ouvrages aux titres évocateurs tels que The Conversion of Swerers,6 An Invectyve agenst the Moost Wicked & Detestable Vyce of Swearing,1 A Swoord agaynst Swearyng,* ou A Sworde against Swearers and Blasphemers,9 on est amené à conclure que, à l'époque de Shakespeare, l'usage de la langue est réglementé...

La tolérance, de Spinoza à Locke

Pour bien concevoir (et mettre en œuvre) la tolérance, il est nécessaire de l'appuyer sur une théorie politique et sur une épistémologie cohérentes. Spinoza, Locke et Bayle offrent en un autre siècle des liens dont il ne serait pas inutile de s'inspirer, notamment le respect de la séparation des champs, des points de vue, des méthodologies. Ce n'est pas parce que le concret est un que son étude peut être une.In order to rightly conceive (and apply) toleration, one must found it on clear epistemological and political theories. In their own age, Spinoza, Locke and Bayle link toleration which such theories, and it could be helpful to follow their suggestions : separation of powers, of aspects, of methodologies. In spite of the fact that the real world is unified, its knowledge must be multifarious

Magneto-optical response in bimetallic metamaterials

We demonstrate resonant Faraday polarization rotation in plasmonic arrays of bimetallic nano-ring resonators consisting of Au and Ni sections. This metamaterial design allows to optimize the trade-off between the enhancement of magneto-optical effects and plasmonic dissipation. Although Ni sections correspond to as little as ~6% of the total surface of the metamaterial, the resulting magneto-optically induced polarization rotation is equal to that of a continuous film. Such bimetallic metamaterials can be used in compact magnetic sensors, active plasmonic components and integrated photonic circuits