Attitude stabilization of a rigid spacecraft in the geomagnetic field

An analytical method is proposed to study the attitude stability of a triaxial spacecraft moving in a circular Keplerian orbit in the geomagnetic field. The method is developed based on the electrodynamics effect of the influence of the Lorentz force acting on the charged spacecraft's surface. We assume that the rigid spacecraft is equipped with an electrostatic charged protective shield, having an intrinsic magnetic moment. The main elements of this shield are an electrostatic charged cylindrical screen surrounding the protected volume of the spacecraft. The rotational motion of the spacecraft about its centre of mass due to torques from gravitational force, as well Lorentz and magnetic forces is investigated. The equilibrium positions of the spacecraft in the orbital coordinate system are obtained. The necessary and sufficient conditions for the stability of the spacecraft's equilibrium positions are constructed using Lyapunov's direct method. The numerical results have shown that the Lorentz force has a significant influence on the stability of the equilibrium positions, which can affect the attitude stabilization of the spacecraft. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Spacecraft's attitude prediction: solar radiation torque and the Earth's shadow

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite, under the influence of torque due to the solar radiation pressure, and taking into account the influence of Earth's shadow. Using Andoyer variables the equations for the rotational motion are presented in extended Hamiltonian form. In order to get a solution for the state variables close to an actual motion, the considered model for the shadow function takes into account physical and geometric factors and three specific regions: shadow, penumbra and full light. A mapping for the shadow function is proposed and a semi-analytical process is applied. When the satellite is totally illuminated or it is inside the penumbra, a known analytical solution is used to compute the satellite's attitude. A numerical simulation shows, when the penumbra region is included, the attenuation of the rotational motion during the transition from the shadow to the illuminate region and vice versa. (c) 2005 Published by Elsevier Ltd on behalf of COSPAR.

Environmental torques acting on a low Earth orbiter cylindrical spacecraft

Classical models of gravity gradient, solar radiation, aerodynamic and magnetic torques acting on a circular cylinder satellite. The magnitude of each such are compared with parameterization in terms of the dimensions of the satellite and its altitude in relation to the Earth's surface. Two different satellite data are considered. The results agree with the classical results and show that for altitude between 0 and 800 km the gravity gradient, aerodynamic and magnetic torques decrease with altitude while the solar radiation torque is almost independent of the altitude. The relative importance of these torques depends on the size, mass, moments of inertia and altitude of the satellite. The results can be useful to propagate the satellite attitude, to satellite missions analysis and to validate the analytical approaches. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Optimal attitude corrections for cylindrical spacecraft

A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.

Short-Term Effects of the Use of Non-Rigid Tools for Postural Control by Adults with Intellectual Disabilities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The rigid-flexible nonlinear robotic manipulator: Modeling and control

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Electron transfer by singlet excited state of porphyn and electron acceptor affinity in rigid medium: photoacoustic phase angle analysis

A espectroscopia fotoacústica obtém informações sobre amplitude e fase, da resposta de um sistema submetido a excitação por luz. Este artigo apresenta estudos do ângulo de fase no processo de transfereência de elétrons entre octaetilporfirina (OEP) e derivados de quinona ambos dispersos em uma matriz polimérica. Observou-se uma tendência no comportamento da fase para valores menores na região espectral próximo de 620 nm. Enquanto que para comprimentos de onda menores este efeito não foi apresentado. Estas medidas sugerem que a transferência de elétrons para o aceitador ocorreu com a participação do estado singleto excitado da octaetilporfirina.

A SIMPLE NUMERICAL-METHOD FOR HYDROSTATIC INCOMPRESSIBLE MODELS WITH RIGID LIDS

A simple and easily implemented method is developed to keep the vertical velocity equal to zero at the bottom and top of hydrostatic incompressible numerical models. The pressure is computed at the top by correcting its value given in the previous time step so that the vertical integral of the horizontal divergence is zero at each column. Numerical experiments that exhibit small time variations of pressure at the top are able to simplify the algorithm and save computer time. Numerical simulations illustrate the method effectiveness for a horizontal deformation-induced frontogenesis.

Batch, sequential and hybrid approaches to spacecraft sensor alignment estimation

Two Kalman-filter formulations are presented for the estimation of spacecraft sensor misalignments from inflight data. In the first the sensor misalignments are part of the filter state variable; in the second, which we call HYLIGN, the state vector contains only dynamical variables, but the sensitivities of the filter innovations to the misalignments are calculated within the Kalman filter. This procedure permits the misalignments to be estimated in batch mode as well as a much smaller dimension for the Kalman filter state vector. This results not only in a significantly smaller computational burden but also in a smaller sensitivity of the misalignment estimates to outliers in the data. Numerical simulations of the filter performance are presented.

A thermodynamics description of the system with N massive parallel rigid wires

In this work, the behaviour of the system with N massive parallel rigid wires is analysed. The aim is to explore its resemblance to a system of multiple cosmic strings. Assuming that it behaves like a 'gas' of massive rigid wires, we use a thermodynamics approach to describe this system. We obtain a constraint relating the linear mass density of the massive wires, the number of the massive wires in the system and the dispersion velocity of the system. © 1996 IOP Publishing Ltd.

Batch and filter approaches to spacecraft sensor alignment estimation

Two Kalman-filter formulations are presented for the estimation of spacecraft sensor misalignments from inflight data. In the first the sensor misalignments are part of the filter state variable; in the second the state vector contains only dynamical variables, but the sensitivities of the filter innovations to the misalignments are calculated within the Kalman filter. This procedure permits the misalignments to be estimated in batch mode as well as a much smaller dimension for the Kalman filter state vector. This results not only in a significantly smaller computational burden but also in a smaller sensitivity of the misalignment estimates to outliers in the data. Numerical simulations of the filter performance are presented.

Rigid internal fixation with titanium versus bioresorbable miniplates in the repair of mandibular fractures in rabbits

The purpose of this study was to compare by qualitative histology the efficacy of rigid internal fixation with titanium system and the Lacto Sorb® system in mandibular fractures in rabbits. Thirty male adult rabbits Oryctolagus cuniculus were used. Unilateral mandibular osteotomies were performed between the canine and first premolar. The animals were divided into two groups: for Group I - rigid internal fixation was performed with titanium system 1.5 mm (Synthes, Oberdorf, Switzerland), with two screws of 6 mm (bicortical) on each side of the osteotomy. For Group II-rigid internal fixation was performed with PLLA/PGA system 1.5 mm (Lacto Sorb®, WLorenz, Jacksonville, FL, USA). The histological analysis evaluated the presence of inflammatory reaction, degree of bone healing and degree of resorption of the Lacto Sorb® screws. The results of both fixation systems were similar, only with a small difference after 15 and 30 days. In Group I a faster bony healing was noted. But after 60 days, bony healing was similar in both groups. It is concluded that both PLLA/PGA and titanium plates and screws provide sufficient strength to permit mandibular bone healing. The resorption process of PLLA/PGA osteosynthesis material did not cause acute or chronic inflammatory reaction or foreign body reaction during the studied period. © 2004 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.