Application of Computer Algebra to Investigation of Equilibrium Orientations of Satellite Subject to Gravitational and Constant Torques
The equilibrium orientations of a satellite in a circular orbit under the influence of gravitational and constant torques are investigated. The stationary motions of a satellite are governed by a set of nonlinear algebraic equations. A computer algebra method based on algorithm for the construction Groebner basis is proposed for determining the equilibrium orientations of a satellite with a given constant torque vector and given principal central moments of inertia. It is shown that 24 isolated equilibrium orientations exist when the module of constant vector is sufficiently small. The equilibrium orientations are determined by algebraic equation of the sixth degree and are analyzed numerically.
Influence of Constant Torque on Equilibria of Satellite in Circular Orbit
We consider the equilibria of a satellite in a circular orbit under the action of gravitational and constant torques. The number of equilibria depending on the parameters of the problem is found by the analysis of an algebraic equation of order 6. The domains with different numbers of equilibria are specified, and the equations of boundary curves are determined in function of values of the components of constant torque. Classification of different distributions of number of equilibria is made for arbitrary values of the parameters.
The peculiar thermo-structural behavior of the anionic lipid DMPG.
Aqueous dispersions of the anionic phospholipid dimyristoyl phosphatidylglycerol (DMPG), around 100 mM ionic strength, are known to exhibit a thermal behavior similar to that of the largely studied lipid dimyristoyl phosphatidylcholine (DMPC), which undergoes a gel to liquid crystalline phase transition at 23 degrees C, well characterized by differential scanning calorimetry (DSC), and other methods. However, at low ionic strength, DMPG has been shown to present a large gel-fluid transition region, ranging from 18 to 35 degrees C. This intermediate phase is optically transparent and characterized by a continuous change in membrane packing. Structural properties of the DMPG gel-fluid transition region will be discussed, based on results obtained by several techniques: electron spin resonance (ESR) of spin labels at the membrane surface and intercalated at different depths in the bilayer; light scattering; DSC; small angle X-ray scattering (SAXS); and fluorescence spectroscopy of probes in the bilayer.