The equilibria and stability of a dynamically symmetrical satellite with a two-degree-of-freedom powered gyroscope

For a dynamically symmetrical satellite carrying a two-degree-of-freedom powered gyroscope, all the relative equilibria in a circular orbit are found as a function of the angular momentum of the rotor and the angle between the precession axis of the gyroscope and the plane of dynamical symmetry. The case with no spring on the axis of the gyroscope frame and the case with a spring whose stiffness satisfies definite conditions are considered. The secular stability of the equilibria is investigated. For a system with dissipation in the axis of the gyroscope frame, the Barbashin–Krasovskii theorem is used to perform a detailed analysis, which enables the character of the Lyapunov stability of all the equilibria to be determined, with the exception of a few points. The results of a numerical solution of the problem of the optimal values of the system parameters, for which asymptotically stable equilibria are obtained with maximum speed, are presented.     

Analysis of the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame

A method that enables a conclusion to be drawn regarding the nature of the Lyapunov stability of the equilibria positions of autonomous systems with partial dissipation from the nature of the secular stability and truncated equations of the linear approximation is developed based on the Barbashin–Krasovskii theorem. The method is used to investigate the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame in a circular orbit. For the case when the axis of the gyroscope frame is oriented parallel to one of the principal axes of inertia of the satellite, the nature of the Lyapunov stability of all the equilibria, with the exception of a few branching points, is determined. It is established that gyroscopic stabilization, which is possible when there is no dissipation in the axis of the frame for certain equilibria that are unstable in the secular sense, breaks down when dissipation occurs.     

Synthesis and chemistry of new spiro‐Δ1‐pyrazoline

In explorations of syntheses and chemistry of spiroheterocycles, we found that the reaction of 2‐diazopropane with (E)‐α‐arylidenepyrrolin‐2‐one, (E)‐α‐arylidene‐γ‐butyrolactone, and (E)‐arylidene‐N‐arylsuccinimide derivatives produced spiro‐Δ¹‐pyrazolines. The photolysis of Δ¹‐pyrazolines has led to cyclopropanes. The structures of the obtained adducts have been assigned by means of spectroscopic measurements. J. Heterocyclic Chem., (2011).     

The effect of activated fillers on the properties of styrene–acrylic adhesives

Results of kaolin modification by thermal activation, sonication and 3% solution of acetic acid are considered. It is shown that the introduction of thermally activated kaolin to compositions based on styrene–acrylic filming agents increases the adhesion characteristics by 1.25–1.4 times (for steel and cement–sand surfaces) and cohesive strength by 1.5–2 times.     

On the higher-order strong isochronism of Cauchy-Riemann systems with homogeneous polynomial perturbations of a linear center

We indicate the maximum order of the general and partial (with an initial polar angle) strong higher-order isochronism of Cauchy-Riemann systems with homogeneous polynomial perturbations of a linear center.     

Structure, thermal, and infrared analyses of [NH3(CH2)3NH3]2[Ni(HP2O7)2(H2O)2] ? 4H2O

[NH₃(CH₂)₃NH₃]₂[Ni(HP₂O₇)₂(H₂O)₂] 4H₂O (NiDAP) is a new diphosphate of transition metallic and organic cations obtained from a mixture of H₄P₂O₇, 2NiCO₃ Ni(OH)₂ 4H₂O and NH₂(CH₂)₃NH₂ in a 1:1/6:1 molar ratio. This mixed organo-mineral compound crystallizes in the triclinic system, P¯, with the unit cell dimensions: a = 7.3678(3)~Å, b = 7.8018(5)Å, c = 11.1958(7)Å, = 76.914(4), = 81.052(4), = 85.46(1), V = 618.57(6)ų and Z = 1. The crystal structure of NiDAP consists of a complex anion, [Ni(HP₂O₇)₂(H₂O)₂]^4– and a diammoniumpropane cation. The complex anion is built up from two neutral water molecules (OW1) and two diphosphosphoric anions coordinated to Ni(II) in a bidentate chelating manner. (OW1) molecules link anionic complexes, [Ni(HP₂O₇)₂(H₂O)₂]^4– to create a thick bidimensional layers parallel to the (a, b) plane. These layers are interconnected in three dimensions through hydrogen bonds established between organic cations, the remaining water molecules OW2, OW3, and some external oxygen atoms of the anionic complex arrays. NiDAP was also characterized by IR spectroscopy, TG-DTA, and DSC analyses.     

An inverse gas chromatographic characterization of polypyrrole-coated poly(vinyl chloride) powder particles

Polypyrrole-coated poly(vinyl chloride) powder particles (PPy-PVC) were prepared by the in-situ chemical polymerization of pyrrole in aqueous solutions in the presence of PVC powder particles using the method of Ouyang and Chan [Polymer 39 (1998) 1857] and characterized by inverse gas chromatography (IGC). By employing n-alkane, 1-heptene, chloroform and tetrahydrofuran molecular probes, the dispersive and acid–base components of the surface energy of the composite materials were estimated at infinite dilution. The values of the dispersive contribution to the surface energy (γ_S^d), at 50 °C, range from 30.3 to 43.5 mJ/m² for the composites, which is much lower than the value of 83.2 mJ/m² obtained for para-toluene sulfonate-doped polypyrrole (PPyTS) bulk powder. This indicates that the injected molecules probe both polypyrrole and the underlying PVC, thus indicating that the conducting polymer is rather patchy at the surface of the insulating polymer substrate. This conclusion supports the previous results obtained by X-ray photoelectron spectroscopy (XPS) [19], indicating that both the coating PPyTS and the substrate PVC are detected by their elemental markers nitrogen and sulfur, and chlorine, respectively.     

New materials derivatives of tetrathiapentalene functionalized by amide groups: Synthesis,characterization, and electrical study

A new series of bis-fused tetrathiafulvalene containing functional groups was synthesized. The synthesis was carried out by using routes involving cross coupling, reduction, and oxidation reactions. The identity of these new donors is confirmed by ¹ Wudl, F.; Smith, G. M.; Hufnagel, E. J. J. Chem. Soc. Chem. Commun. 1970, 21, 1453-1454.[Crossref] , [Google Scholar] H NMR spectroscopy, mass spectrometry, and elemental analysis. We have used the cyclic voltammetry in order to determine the character π-donors of these molecules and to verify the reversibility of the redox process involved. Molecular orbital diagram has been calculated using density-functional calculations. Charge transfer complexes with tetracyanoquinodimethane (TNQ) were prepared by chemical redox reactions.     

Recovering boundary data: The Cauchy Stokes system

This paper is concerned with the severely ill-posed Cauchy–Stokes problem. We are interested in a data completion problem which is exploited to detect small leaks to control water loss Kim et al. (2008) [1]. This inverse problem is rephrased into an optimization one: An energy-like error functional is introduced. We prove that the optimality condition of the first order is equivalent to solving an interfacial equation which turns out to be a Cauchy-Steklov-Poincaré operator. Numerical trials highlight the efficiency of the method.