http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/732892.htmlData aggregation is an essential operation to reduce energy consumption in large-scale wireless sensor networks (WSNs). A compromised node may forge an aggregation result and mislead base station into trusting a false reading. Efficient and secure aggregation scheme is critical in WSN applications due to the stringent resource constraints. In this paper, we propose a method to build up the representative-based aggregation tree in the WSNs such that the sensing data are aggregated along the route from the leaf cell to the root of the tree. In the cinema of large-scale and high-density sensor nodes, representative-based aggregation tree can reduce the data transmission overhead greatly by directed aggregation and cell-by-cell communications. It also provides security services including the integrity, freshness, and authentication, via detection mechanism in the cells.Yanfei Zheng, Kefei Chen, and Weidong Qiu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/962351.htmlThe quasistatic bending response is presented for a simply supported functionally graded rectangular plate subjected to a through-the-thickness temperature field under the effect of various theories of generalized thermoelasticity, namely, classical dynamical coupled theory, Lord and Shulman's theory with one relaxation time, and Green and Lindsay's theory with two relaxation times. The generalized shear deformation theory obtained by the first author is used. Material properties of the plate are assumed to be graded in the thickness direction according to a simple exponential law distribution in terms of the volume fractions of the constituents. The numerical illustrations concern quasistatic bending response of functionally graded square plates with two constituent materials are studied using the different theories of generalized thermoelasticityA. M. Zenkour, D. S. Mashat, and K. A. Elsibai© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/498249.htmlThe variational iteration algorithm combined with the exp-function method is suggested to solve the generalized Benjamin-Bona-Mahony equation (BBM) with variable coefficients. Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered.Cesar A. Gómez and Alvaro H. Salas© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/149385.htmlModel-based analysis and synthesis applied to the dynamics, guidance, and control of an autonomous undersea vehicle are presented. As the dynamic model for describing vehicle motion mathematically, the equations of motion are derived. The stability derivatives in the equations of motion are determined by a simulation-based technique using computational fluid dynamics analysis. The dynamic model is applied to the design of the low-level control systems, offering model-based synthetic approach in dynamics and control applications. As an intelligent navigational strategy for undersea vehicles, we present the optimal guidance in environmental disturbances. The optimal guidance aims at the minimum-time transit of a vehicle in an environmental flow disturbance. In this paper, a newly developed algorithm for obtaining the numerical solution of the optimal guidance law is presented. The algorithm is a globally working procedure deriving the optimal guidance in any deterministic environmental disturbance. As a fail-safe tactic in achieving the optimal navigation in environments of moderate uncertainty, we propose the quasi-optimal guidance. Performances of the optimal and the quasi-optimal guidances are demonstrated by the simulated navigations in a few environmental disturbances.Kangsoo Kim and Tamaki Ura© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/740460.htmlHerein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness (J2) and the equatorial ellipticity (sectorial term C22). Using Lie-Hori method up to the second order short-period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun-synchronous polar lunar orbit is presented.Jean Paulo dos Santos Carvalho, Rodolpho Vilhena de Moraes, and Antônio Fernando Bertachini de Almeida Prado© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/249162.htmlCoupled first-order IVPs are frequently used in many parts of engineering and sciences. We present a “solver” including three computer programs which were joint with the MATLAB software to solve and plot solutions of the first-order coupled stiff or nonstiff IVPs. Some applications related to IVPs are given here using our MATLAB-linked solver. Muon catalyzed fusion in a D-T mixture is considered as a first dynamical example of the coupled IVPs. Then, we have focused on the fuel depletion in a suggested PWR including poisons burnups (xenon-135 and samarium-149), plutonium isotopes production, and uranium depletion.F. Faghihi and M. Saidi Nezhad© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/826721.htmlGlobal synchronization in adaptive coupling networks is studied in this paper. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with different topologies.Zhengzhong Yuan, Jianping Cai, and Meili Lin© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/107538.htmlWe address a neural-oscillator-based control scheme to achieve biologically inspired motion generation. In general, it is known that humans or animals exhibit novel adaptive behaviors regardless of their kinematic configurations against unexpected disturbances or environment changes. This is caused by the entrainment property of the neural oscillator which plays a key role to adapt their nervous system to the natural frequency of the interacted environments. Thus we focus on a self-adapting robot arm control to attain natural adaptive motions as a controller employing neural oscillators. To demonstrate the excellence of entrainment, we implement the proposed control scheme to a single pendulum coupled with the neural oscillator in simulation and experiment. Then this work shows the performance of the robot arm coupled to neural oscillators through various tasks that the arm traces a trajectory. With these, the real-time closed-loop system allowing sensory feedback of the neural oscillator for the entrainment property is proposed. In particular, we verify an impressive capability of biologically inspired self-adaptation behaviors that enables the robot arm to make adaptive motions corresponding to an unexpected environmental variety.Woosung Yang, Jaesung Kwon, Nak Young Chong, and Yonghwan Oh© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/649028.htmlThe environmental factors are receiving increasing attention in different life cycle stages of products. When a product reaches its End-Of-Life (EOL) stage, the management of its recovery process is affected by the environmental and also economical factors. Selecting efficient methods for the collection and recovery of EOL products has become an important issue. The European Union Directive 2000/53/EC extends the responsibility of the vehicle manufacturers to the postconsumer stage of the vehicle. In order to fulfill the requirements of this Directive and also efficient management of the whole recovery process, the conceptual framework of a reverse logistics network is presented. The distribution of new vehicles in an area and also collecting the End-of-Life Vehicles (ELVs) and their recovery are considered jointly. It is assumed that the new vehicles distributors are also responsible for collecting the ELVs. Then a mathematical model is developed which minimizes the costs of setting up the network and also the relevant transportation costs. Because of the complexity of the model, a solution methodology based on the genetic algorithm is designed which enables achieving good quality solutions in a reasonable algorithm run time.Masoud Zarei, Saeed Mansour, Ali Husseinzadeh Kashan, and Behrooz Karimi© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/209780.htmlReduced-order models have a number of practical engineering applications for unsteady flows that require either low-dimensional approximations for analysis and control or repeated simulation over a range of parameter values. The standard method for building reduced-order models uses the proper orthogonal decomposition (POD) and Galerkin projection. However, this standard method may be inaccurate when used “off-design” (at parameter values not used to generate the POD). This phenomena is exaggerated when parameter values describe the shape of the flow domain since slight changes in shape can have a significant influence on the flow field. In this paper, we investigate the use of POD sensitivity vectors to improve the accuracy and dynamical system properties of the reduced-order models to problems with shape parameters. To carry out this study, we consider flows past an elliptic cylinder with varying thickness ratios. Shape sensitivities (derivatives of flow variables with respect to thickness ratio) computed by finite-difference approximations are used to compute the POD sensitivity vectors. Numerical studies test the accuracy of the new bases to represent flow solutions over a range of parameter values.Imran Akhtar, Jeff Borggaard, and Alexander Hay© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/969714.htmlWe solve the positioning problem of a spherical microparticle trapped by Optical Tweezers, under the assumption that the drag viscous force is presented. To do it, we develop two control strategies for the manipulation of this kind of optical trap. The first control strategy is developed assuming that the damping coefficient is known, while in the second strategy this parameter value is only partially known, which in practice it is more realistic due to the difficulty to estimate it. Both strategies are based on the traditional Lyapunov method in conjunction with the use of a saturation function. The stability analysis of both strategies was carried out by using the standard Lyapunov stability theory. Finally, numerical simulations validate the effectiveness of both control approaches in reducing the random position fluctuations produced by the inherent thermal noise.Carlos Aguilar-Ibañez and Luis I. Rosas-Soriano© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/924275.htmlThe flight dynamic equations in mathematics for aircraft response to the adverse weathers, such as wind shear, atmospheric turbulence, and in-flight icing, are nonlinear and unsteady. To effectively analyze the performance degradation and variations in stability of commercial aircraft that encountered these weather hazards, the nonlinear and dynamic (i.e., time dependent) aerodynamic models based on flight data would be needed. In the present paper, a numerical modeling method based on a fuzzy-logic algorithm will be presented to estimate the aerodynamic models for a twin-jet transport by using the flight data from the flight data recorder (FDR). The aerodynamic models having the capability to generate continuous stability derivatives, especially for sensitivity study of unknown factors in adverse weather conditions, will be demonstrated in this paper.Ray C. Chang, Cun-En Ye, C. Edward Lan, and Yannian Lee© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/913147.htmlFor modeling and controlling dynamic phenomena it is important to establish with higher accuracy some significant quantities corresponding to the dynamic system. For fast phenomena, such significant quantities are represented by the derivatives of the received signals. In case of advanced computer modeling, the received signal should be filtered and converted into a time series corresponding to the estimated values for the dynamic system through a sampling procedure. This paper will show that present-day methods for computing in a robust manner the first derivative of a received signal (using an oscillating system working on a limited time interval and a supplementary differentiation method) can be extended to the robust computation of higher order derivatives of the received signal by using a specific set of second-order oscillating systems (working also on limited time intervals) so as estimative values for higher-order derivatives are to be directly generated (avoiding the necessity of additional differentiation or amplifying procedures, which represent a source of supplementary errors in present-day methods).Andreea Sterian and Alexandru Toma© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/384071.htmlA simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.André Fenili, Luiz Carlos Gadelha de Souza, and Bernd Schäfer© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/303604.htmlSwing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spacecrafts. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct link between low Earth orbits and the lunar sphere of influence to get low-energy transfer trajectories to the Near Earth Objects (NEOs) 99942 Apophis, 1994 WR12, and 2007 UW1 through swing-bys with the Moon. The existence of this link is related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in this link are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. Therefore, the trajectories have sufficient reach to intercept the NEOs' orbits.C. F. de Melo, E. E. N. Macau, and O. C. Winter© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/361860.htmlThis paper addresses the cryptanalysis of a secure communication scheme proposed by Wu (2006), where the information signal is modulated into a system parameter of a unified chaotic system. It is demonstrated that a parameter observer can be designed to identify the parameter determined by the transmitted information and then the transmitted information can be obtained. Compared with the existing analysis using adaptive observer, the cryptanalysis based on parameter observer is much simpler and needs less structure information of the transmitter system. With numerical simulations, it is shown that the parameter observer has stronger practicality and robustness. Furthermore, it is still possible to obtain the transmitted information, even if the derivative of the transmitted signal is unknown.Haipeng Peng, Yan Shao, Lixiang Li, and Yixian Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/897570.htmlSeveral irregular satellites of the giant planets were found in the last years. Their orbital configuration suggests that these satellites were asteroids captured by the planets. The restricted three-body problem can explain the dynamics of the capture, but the capture is temporary. It is necessary some kind of dissipative effect to turn the temporary capture into a permanent one. In this work we study an asteroid suffering a gas drag at an extended atmosphere of a planet to turn a temporary capture into a permanent one. In the primordial Solar System, gas envelopes were created around the planet. An asteroid that was gravitationally captured by the planet got its velocity reduced and could been trapped as an irregular satellite. It is well known that, depending on the time scale of the gas envelope, an asteroid will spiral and collide with the planet. So, we simulate the passage of the asteroid in the gas envelope with its density decreasing along the time. Using this approach, we found effective captures, and have a better understanding of the whole process. Finally, we conclude that the origin of the irregular satellites cannot be attributed to the gas drag capture mechanism alone.E. Vieira Neto and O. C. Winter© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/879519.htmlIn this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations. The second problem is concerned with the flutter phenomena in aircraft wings in a subsonic, incompressible, inviscid air flow. It has been shown numerically that there exists a pair of the aeroelastic modes whose behavior depends on a speed of an air flow. Namely, when the speed increases, the distance between the modes tends to zero, and at some speed that can be treated as the flutter speed these two modes merge into one double mode.Marianna A. Shubov, Stephen Wineberg, and Robert Holt© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/471804.htmlRolling-element bearings are simple machine elements of great utility used both in simple commercial devices as in complex engineering mechanisms. Because of being a very popular machine element, there is a lot of literature on the subject. With regard to the behavior of internal loading distribution, elastic deformations at point or line contacts, and geometric parameters under loading, although there are many works describing the parameters variation models, few works show such variations in practice, even under simple static loadings. In an attempt to cover this gap some studies are being developed in parallel. Particularly in this work, a new, iterative computational procedure is introduced which calculates internal normal ball loads in statically loaded single-row, angular-contact ball bearings, subjected to a known thrust load which is applied to a variable distance (lever arm or eccentricity) from the geometric bearing center line. Numerical examples results for a 218 angular-contact ball bearing have been compared with those from the literature. Fifty figures are presented showing geometrical features and the following parameters variations as functions of the thrust load and eccentricity: contact angle, contact ellipse parameters, normal ball loads, distances between groove curvature centers, normal and axial deflections, and loading zones.Mário César Ricci© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/181360.htmlThe spatial equilateral restricted four-body problem (ERFBP) is a four body problem where a mass point of negligible mass is moving under the Newtonian gravitational attraction of three positive masses (called the primaries) which move on circular periodic orbits around their center of mass fixed at the origin of the coordinate system such that their configuration is always an equilateral triangle. Since fourth mass is small, it does not affect the motion of the three primaries. In our model we assume that the two masses of the primaries m2 and m3 are equal to μ and the mass m1 is 1−2μ. The Hamiltonian function that governs the motion of the fourth mass is derived and it has three degrees of freedom depending periodically on time. Using a synodical system, we fixed the primaries in order to eliminate the time dependence. Similarly to the circular restricted three-body problem, we obtain a first integral of motion. With the help of the Hamiltonian structure, we characterize the region of the possible motions and the surface of fixed level in the spatial as well as in the planar case. Among other things, we verify that the number of equilibrium solutions depends upon the masses, also we show the existence of periodic solutions by different methods in the planar case.Martha Álvarez-Ramírez and Claudio Vidal© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/936081.htmlIn the recent years, much attention has been paid to the research and development of structural control techniques with particular emphasis on alleviation of wind and seismic responses of buildings and bridges in China. Structural control in civil engineering has been developed from the concept into a workable technology and applied into practical engineering structures. The aim of this paper is to review a state of the art of researches and applications of structural control in civil engineering in China. It includes the passive control, active control, hybrid controland semiactive control. Finally, the possible future directions of structural control in civil engineering in China are presented.Hongnan Li and Linsheng Huo© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/742894.htmlFuruta's pendulum has been an excellent benchmark for the automatic control community in the last years, providing, among others, a better understanding of model-based Nonlinear Control Techniques. Since most of these techniques are based on invariants and/or integrals of motion then, the dynamic model plays an important role. This paper describes, in detail, the successful dynamical model developed for the available laboratory pendulum. The success relies on a basic dynamical model derived from Classical Mechanics which has been augmented to compensate the non-conservative torques. Thus, the quasi-conservative “practical” model developed allows to design all the controllers as if the system was strictly conservative. A survey of all the nonlinear controllers designed and experimentally tested on the available laboratory pendulum is also reported.J. Á. Acosta© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/760479.htmlWe study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs). The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.L. I. Manevitch, A. S. Kovaleva, and E. L. Manevitch© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/109501.htmlWe deal with the effect of Unified Power Flow Controller (UPFC) installation on the objective function of an electricity market. Also this paper proposes a Novel UPFC modelling in OPF which facilities the consideration of the impact of four factors on power market. These include the series transformer impedance addition, the shunt reactive power injection, the in-phase component of the series voltage and the quadrature component of the series voltage. The impact of each factor on the electricity market objective function is measured and then compared with the results from a sensitivity approach. The proposed sensitivity approach is fast so it does not need to repeat OPF solutions. The total impacts of the factors are used to offer UPFC insertion candidate points. It is shown that there is a clear match between the candidate points of the sensitivity method and those proposed by the introduced UPFC modelling in our test case. Furthermore, based on the proposed method, the relation between settings of UPFC series part and active and reactive power spot prices is presented.Seyed Abbas Taher and Ali Akbar Abrishami© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/397454.htmlThis paper points out that the predictability analysis of conventional time series may in general be invalid for long-range dependent (LRD) series since the conventional mean-square error (MSE) may generally not exist for predicting LRD series. To make the MSE of LRD series prediction exist, we introduce a generalized MSE. With that, the proof of the predictability of LRD series is presented in Hilbert space.Ming Li and Jia-Yue Li© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2010/901095.htmlThe main purpose of the present study is to investigate the possible application of decision tree in landslide susceptibility assessment. The study area having a surface area of 174.8 km2 locates at the northern coast of the Sea of Marmara and western part of Istanbul metropolitan area. When applying data mining and extracting decision tree, geological formations, altitude, slope, plan curvature, profile curvature, heat load and stream power index parameters are taken into consideration as landslide conditioning factors. Using the predicted values, the landslide susceptibility map of the study area is produced. The AUC value of the produced landslide susceptibility map has been obtained as 89.6%. According to the results of the AUC evaluation, the produced map has exhibited a good enough performance.H. A. Nefeslioglu, E. Sezer, C. Gokceoglu, A. S. Bozkir, and T. Y. Duman© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/140963.htmlHerein, the purpose is to present a Kalman filter based on the sigma point unscented transformation development, aiming at real-time satellite orbit determination using GPS measurements. First, a brief review of the extended Kalman filter will be done. After, the sigma point Kalman filter will be introduced as well as the basic idea of the unscented transformation, in which this filter is based. Following, the unscented Kalman filter applied to orbit determination will be explained. Such explanation encloses formulations about the orbit determination through GPS; the dynamic model; the observation model; the unmodeled acceleration estimation; also an application of this new filter approaches on orbit determination using GPS measurements discussion.Paula Cristiane Pinto Mesquita Pardal, Helio Koiti Kuga, and Rodolpho Vilhena de Moraes© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/537256.htmlWe study orbital dynamics of a compound solar sail, namely, a Simple Solar Photon Thruster and compare its behavior to that of a common version of sailcraft. To perform this analysis, development of a mathematical model for force created by light reflection on all sailcraft elements is essential. We deduce the equations of sailcraft's motion and compare performance of two schemes of solar propulsion for two test time-optimal control problems of trajectory transfer.Anna D. Guerman, Georgi V. Smirnov, and Maria Cecilia Pereira© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/242396.htmlAn analytical approach for spin-stabilized satellites attitude propagation is presented, considering the influence of the residual magnetic torque and eddy currents torque. It is assumed two approaches to examine the influence of external torques acting during the motion of the satellite, with the Earth's magnetic field described by the quadripole model. In the first approach is included only the residual magnetic torque in the motion equations, with the satellites in circular or elliptical orbit. In the second approach only the eddy currents torque is analyzed, with the satellite in circular orbit. The inclusion of these torques on the dynamic equations of spin stabilized satellites yields the conditions to derive an analytical solution. The solutions show that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spacecraft's spin axis and the eddy currents torque causes an exponential decay of the angular velocity magnitude. Numerical simulations performed with data of the Brazilian Satellites (SCD1 and SCD2) show the period that analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of Brazil National Research Institute.Roberta Veloso Garcia, Maria Cecília F. P. S. Zanardi, and Hélio Koiti Kuga© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/185965.htmlA shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.Chi-Min Liu© 2010, Hindawi Publishing Corporation. All rights reserved.