Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Tillering dynamics in Guinea grass pastures subjected to management strategies under rotational grazing

This study was carried out to analyze the tillering profile of Guinea grass (Panicum maximum cv. Tanzania) pastures subjected to two grazing frequencies (time necessary to intercept 90 and 95% of the incoming light) and two post-grazing heights (30 and 50 cm) in the period from November 2005 to October 2006. The experimental design was of completely randomized blocks with three replications, in a 2 × 2 factorial arrangement. At the end of the spring, pastures managed with 90% light interception showed greater tiller appearance rates in relation to pastures managed with 95%, regardless of post-grazing height. In the summer and fall, pastures managed with post-grazing height of 30 cm showed higher tiller appearance rates in comparison with pastures managed at 50 cm, regardless of grazing frequency. Concerning the tiller mortality rates, in the summer, higher values were found for pastures managed at 90/50 and 95/30 (interception/height), intermediate values at 90/30 and lower values in those managed at 95/50. Pastures managed at 90/30, 95/30 and 95/50 in the fall presented greater tiller mortality rates than those managed at 90/50. These differences do not occur in the winter/beginning of spring. The stability index remained above 1 all through the experimental period. All management strategies evaluated are adequate for Guinea grass.

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.