The Famatina margin records an orogenic cycle of convergence, metamorphism, magmatism, and extension related to the accretion of the allochthonous Precordillera terrane. New structural, petrologic, and geochronologic data from the Loma de Las Chacras region demonstrate two distinct episodes of lower crustal migmatization. The first event preserves a counterclockwise pressure-temperature path in kyanite-K-feldspar pelitic migmatites that resulted in lower crustal migmatization via muscovite dehydration melting at ∼12 kbar and 868 • C at 461 ± 1.7 Ma. The shape of the pressure temperature path and timing of metamorphism are similar to those of regional midcrustal granulites and suggest pervasive Ordovician migmatization throughout the Famatina margin. One-dimensional thermal modeling coupled with regional isotopic data suggests Ordovician melts remained at temperatures above their solidus for 20-30 Ma following peak granulite facies metamorphism, throughout a time period marked by regional oblique convergence. The onset of synconvergent extension occurred only after regional migmatites cooled beneath their solidus and was synchronous with the cessation of Precordillera terrane accretion at ∼436 Ma. The second migmatite event was regionally localized and occurred at ∼700 • C and 12 kbar between 411 and 407 Ma via vapor saturated melting of muscovite. Migmatization was synchronous with extension, exhumation, and strike-slip deformation that likely resulted from a change in the plate boundary configuration related to the convergence and collision of the Chilenia terrane.
The full kinematic properties of a minimal set of rigid body attitude coordinates called Symmetric Stereographic Orientation Parameters (SSOPs) are developed. These coordinates result from a stereographic projection of the Euler parameter constraint hypersphere onto a three-dimensional hyper-plane. As discussed in previous work [5], this family contains the well-known classical and modified Rodrigues parameters. Considering general SSOP projection points, transformations to the Euler parameters and the direction cosine matrix are discussed. The set of three SSOP coordinates have the unique feature that the associated singularity can be placed at a desired principal rotation angle by adjusting the projection point. In contrast to the Rodrigues parameters, the SSOP coordinates do not represent a unique orientation. The impact of this non-uniqueness on the constrained spacecraft attitude control problem is discussed. An attitude feedback control law in terms of SSOPs will inherently avoid reaching this singular attitude description, and thus constrain the attitude error response to be within a well-defined cone. Lyapunov's direct method is used to illustrate how a SSOP-based control law can be derived to drive the spacecraft attitude away from the singularity and towards a desired orientation. This control law generalizes the previously developed classical and modified Rodrigues parameter-based attitude control laws for general stereographic projection points.
We analyze the out-of-plane librations of a tethered satellite system that is nominally rotating in the orbit plane. To isolate the librational dynamics, the system is modeled as two point masses connected by a rigid rod with the system mass center constrained to an unperturbed circular orbit. For small out-of-plane librations, the in-plane motion is unaffected by the out-of-plane librations and a solution for the in-plane motion is determined in terms of Jacobi elliptic functions. This solution is used in the linearized equation for the out-of-plane librations, resulting in a Hill's equation. Floquet theory is used to analyze the Hill's equation, and we show that the out-of-plane librations are unstable for certain ranges of in-plane spin rate. For relatively high in-plane spin rates, the out-of-plane librations are stable, and the Hill's equation can be approximated by a Mathieu's equation. Approximate solutions to the Mathieu's equation are determined, and we analyze the dominant characteristics of the out-of-plane librations for high in-plane spin rates. The results obtained from the analysis of the linearized equations of motion are compared to numerical simulations of the nonlinear equations of motion, as well as numerical simulations of a more realistic system model that accounts for tether flexibility. The instabilities discovered from the linear analysis are present in both the nonlinear system and the more realistic system model. The approximate solutions for the out-of-plane librations compare well to the nonlinear system for relatively high in-plane rotation rates, and also capture the significant qualitative behavior of the flexible system.
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