The properties of the steady motions of a body carrying a system of two-degree-of-freedom powered gyroscopes

The steady motions of a rigid body carrying several two-degree-of-freedom powered gyroscopes in a uniform external field are investigated. It is shown that when the installation scheme of the gyroscopes in the carrying body is collinear, the problem of determining the steady motions of the system and analysing their secular stability reduces for the most part to the previously solved, similar problem for a system with one gyroscope. It is established that when there is dissipation in the axes of the gyroscope frames, the system tends asymptotically to a state of rest if the absolute value of the total angular momentum of the system lies in the segment of possible absolute values of the angular momentum of the gyroscope rotors. The results of an analysis of the steady motions of a system carrying two gyroscopes with a non-collinear installation scheme are presented.     

Missing boundary data recovering for the Helmholtz problem

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments. To cite this article: R. Ben Fatma et al., C. R. Mecanique 335 (2007).     

Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes

To study the stability of steady rotations of a control moment gyro system with internal dissipation, we use the Barbashin-Krasovskii theorem and the relation, established in [1], between the Lyapunov function and steady motions. Taking into account the special properties of the original problem, we reduce it to a lower-dimensional problem.We give a detailed presentation of an algorithm for analyzing the stability of steady motions of a gyrostat and use this algorithm to perform a complete study for two systems consisting, respectively, of one and two gyros whose gimbal axes are parallel to the principal axis of inertia of the system. Each steady motion is identified as either asymptotically stable or unstable. We find periodic motions that exist only in the presence of dynamic symmetry and which are regular precessions. For the system with two gyros, we prove the asymptotic stability of quiescent states and prove that in the angular momentum range where these states are defined the system does not have any other stable motions.     

An Aitken-like acceleration method applied to missing boundary data reconstruction for the Cauchy–Helmholtz problem

This Note is concerned with the severely ill-posed Cauchy–Helmholtz problem. This Cauchy problem being rephrased through an “interfacial” equation, we resort to an Aitken–Schwarz method for solving this equation. Numerical trials highlight the efficiency of the present method.     

Adaptive fuzzy control‐based projective synchronization of uncertain nonaffine chaotic systems

This article aims to introduce a projective synchronization approach based on adaptive fuzzy control for a class of perturbed uncertain multivariable nonaffine chaotic systems. The fuzzy‐logic systems are employed to approximate online the uncertain functions. A Lyapunov approach is used to design the parameter adaptation laws and to demonstrate the boundedness of all signals of the closed‐loop system as well as the convergence of the synchronization errors to bounded residual sets. Finally, numerical simulation results are presented to verify the feasibility and effectiveness of the proposed synchronization system based on fuzzy adaptive controller. © 2014 Wiley Periodicals, Inc. Complexity 21: 180–192, 2015     

On the limit cycles for a class of generalized Kukles differential systems

In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $\dot{x}=-y, \hspace{0.2cm} \dot{y}=x-f(x)-g(x)y-h(x)y^{2}-l(x)y^{3},$ where $f(x)=\epsilon f_{1}(x)+\epsilon^{2}f_{2}(x),$ $g(x)=\epsilon g_{1}(x)+\epsilon^{2}g_{2}(x),$ $h(x)=\epsilon h_{1}(x)+\epsilon^{2}h_{2}(x)$ and $l(x)=\epsilon l_{1}(x)+\epsilon^{2}l_{2}(x)$ where $f_{k}(x),$ $g_{k}(x),$ $h_{k}(x)$ and $l_{k}(x)$ have degree $n_{1},$ $n_{2},$ $n_{3}$ and $n_{4},$ respectively for each $k=1,2,$ and $\varepsilon$ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=-y,$ $\dot{y}=x$ using the averaging theory of first and second order.     

Tetranuclear cobalt trimethylacetate Co4(μ3-OH)2(μ-OOCBut)6(C4H6N2O)4 containing coordinated 3-methyl-5-pyrazolone

We found that the reaction of the compound obtained by alloying hydrous cobalt(II) acetate and pivalic acid with 3-methyl-5-pyrazolone in refluxing hexane produces the tetranuclear complex Co₄(μ₃-OH)₂(μ-OOCBu^t)₆·(C₄H₆N₂O)₄·2HOOCBu^t (complex 3). The complex has been structurally characterized using single-crystal X-ray diffraction     

Thermal stability of atmospheric plasma sprayed (Ni, Cu, Co)–YSZ and Ni–Cu–Co–YSZ anodes cermets for SOFC application

This paper reports the results of the thermal stability study of M–YSZ (M=Ni, Cu, Co, Cu–Co, Ni–Cu–Co) SOFC anode cermets materials at different heat treatment temperatures. The cermets were elaborated by atmospheric plasma spraying (APS) with optimized conditions and then submitted to heat treatments at 800 and 1000 °C, respectively. Scanning electron microscopy and X-ray diffraction were used to characterize, respectively, the morphology and structure of obtained films, before and after thermal annealing. A correlation was made between the differential scanning calorimetry analysis results and those obtained by X-ray diffraction. Focusing, in this study, on YSZ matrix thermal stability, the obtained results were as follows: the monometallic cermets with the lowest amount of metal and the trimetallic one exhibited a good stability at 800 °C, whereas at 1000 °C, all considered cermets were unstable with a eutectoid decomposition of YSZ matrix.     

Influence of the solvent on the extraction of copper(II) from nitrate medium using salicylideneaniline

Different solvents including cyclohexane, dichloromethane, chloroform, toluene, 1-octanol, and methyl isobutyl ketone (MIBK) have been evaluated in extracting copper(II) from nitrate medium by salicylideneaniline. Extracted species differs from solvent to solvent: CuL₂ in cyclohexane, toluene, 1-octanol, and methyl isobutyl ketone. However, in dichloromethane or chloroform, there are two complexes of the type CuL₂ and CuL₂(HL). The extraction constants and percentage of extraction (%E) are calculated for different solvents. Solvent played an important role in recovering copper(II) from the aqueous solution, thus affecting the extraction equilibrium and extraction efficiency. The nonpolar solvent showed better performance than the polar solvent. The maximum extraction efficiency was 85.75% at pH?=?4.5, which was from cyclohexane.