Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some orbital characteristics of lunar artificial satellites

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

Artificial satellites orbits in 2:1 resonance: GPS constellation

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

Sub-Optimal Orbital Maneuvers for Artificial Satellites

The determination of a specific orbit and the procedure to calculate orbital maneuvers of artificial satellites are problems of extreme importance in the study of orbital mechanics. Therefore, the transferring problem of a spaceship from one orbit to another, and the attention due to this subject has in increased during the last years. Many applications can be found in several space activities, for example, to put a satellite in a geostationary orbit, to change the position of a spaceship, to maintain a specific satellite's orbit, in the design of an interplanetary mission, and others. The Brazilian Satellite SCD-1 (Data Collecting Satellite) will be used as example in this paper. It is the first satellite developed entirely in Brazil, and it remains in operation to this date. SCD-1 was designed, developed, built, and tested by Brazilian scientists, engineers, and technicians working at INPE (National Institute for Space Research, and in Brazilian Industries. During the lifetime, it might be necessary do some complementary maneuvers, being this one either an orbital transferring, or just to make periodical corrections. The purpose of transferring problem is to change the position, velocity and the satellite's mass to a new pre determined state. This transfer can be totally linked (in the case of "Rendezvous") or partially free (free time, free final velocity, etc). In the global case, the direction, the orientation and the magnitude of the thrust to be applied must be chosen, respecting the equipment's limit. In order to make this transferring, either sub-optimal or optimal maneuvers may be used. In the present study, only the sub-optimal will be shown. Hence, this method will simplify the direction of thrust application, to allow a fast calculation that may be used in real time, with a very fast processing. The thrust application direction to be applied will be assumed small and constant, and the purpose of this paper is to find the time interval that the thrust is applied. This paper is basically divided into three parts: during the first one the sub-optimal maneuver is explained and detailed, the second presents the Satellite SCD-1, and finally the last part shows the results using the sub-optimal maneuver applied to the Brazilian Satellite.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Artificial satellites: Resonance effects produced by terrestrial tide

Effects due to resonances in the orbital motion of artificial satellites disturbed by the terrestrial tide are analyzed. The nodal co-rotation resonance, apsidal co-rotation resonance and the Lidov-Kozai's mechanism are studied. The effects of the resonances are analyzed through the variations of the metric orbital elements. Libration and circulation motions for high orbits with high eccentricities are verified for the Lidov-Kozai's mechanism.

Artificial satellites dynamics: Resonant effects

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J20 and J40 and the tesseral harmonics J22 and J42. Through successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, two critical angles are studied, 2201 and 4211. Numerical results show the time behavior of the semi-major axis and 2 angle.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

Geodetic earth orbiting satellite (GEOS-C) Applications technology satellite (ATS-F) tracking experiment

"NASA TM X-63872."

Learning object dynamics for smooth tracking of moving lip contours

A new technique is proposed for learning the dynamic characteristics of a deformable object, applied in particular to the problem of lip-tracking. Experimental results are given which demonstrate that the use of dynamic models allows the system to track more robustly under adverse conditions and to correct spurious, poorly tracked frames