Spin stabilized satellite's attitude propagation with quaternions

This paper presents a study of a modeling scheme for the spin stabilized satellites attitude, entirely developed in terms of quaternion parametrization. The analysis includes numerical propagation of the rotational motion equation, considering the influence of the following torques: aerodynamic, gravity gradient, residual magnetic, eddy currents and the one due to the Lorentz force. Applications are developed considering the Brazilian Spin Stabilized Satellites SCD1 and SCD2, which are quite appropriated for verification and comparison of the theory with the real data generated and processed by the INPE's Satellite Control Center (SCC). The results show that for SCD1 and SCD2 the influence of the eddy current torque is bigger than the others ones, not only due to the orbit altitude, but also to other specific satellites characteristics. The influence of the torque due to Lorentz force is smaller than the others ones because of the dimension and the electrical charges of the SCD1 and SCD2. In all performed tests the errors remained within the dispersion range specified for the attitude determination system of INPE's SCC. The results show the feasibility of using the quaternion attitude parametrization for modeling the satellite dynamics of spin stabilized satellites.

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute.

Analytical prediction of the spin stabilized satellite's attitude using the solar radiation torque

The aim of this paper is to present an analytical solution for the spin motion equations of spin-stabilized satellite considering only the influence of solar radiation torque. The theory uses a cylindrical satellite on a circular orbit and considers that the satellite is always illuminated. The average components of this torque were determined over an orbital period. These components are substituted in the spin motion equations in order to get an analytical solution for the right ascension and declination of the satellite spin axis. The time evolution for the pointing deviation of the spin axis was also analyzed. These solutions were numerically implemented and compared with real data of the Brazilian Satellite of Data Collection - SCD1 an SCD2. The results show that the theory has consistency and can be applied to predict the spin motion of spin-stabilized artificial satellites.

Efeitos da injunção da base nas orientações interior e exterior e nas coordenadas do espaço objeto em imagens obtidas com a estéreo vídeo-câmara de um sistema móvel de mapeamento

In general, a land-based mobile mapping system is featured by a vehicle with a pair of video cameras mounted on the top and positioning and navigation sensors loaded in the vehicle. Considering the pair of video cameras mounted on the roof of the vehicle as a stereo camera pointing forward with both optical axes parallel to each other and orthogonal to the stereo base, whose length is 0.94 m, this paper aims at analyzing the interior and exterior camera orientation and the object point coordinates estimated by phototriangulation when the length constraint related to the stereo base is considered or not. The results show that the stereo base constraint has effect ouver the convergence estimation, but does it neither improves the object point coordinate estimation at significance level of 5% and nor it influences the interior orientation parameters. Finally, it has been noticed that the optical axes are not truly parallel to each other and orthogonal to the stereo base. Additionally, it has been observed that there is a convergence of approximately 0.5 degrees in the optical axes and they are not in the same plane (approximately 0.8 degrees deviation).

Follicular deviation and acquisition of ovulatory capacity in bovine follicles

Selection of dominant follicles in cattle is associated with a deviation in growth rate between the dominant and largest subordinate follicle of a wave (diameter deviation). To determine whether acquisition of ovulatory capacity is temporally associated with diameter deviation, cows were challenged with purified LH at known times after a GnRH-induced LH surge (experiment 1) or at known follicular diameters (experiments 2 and 3). A 4-mg dose of LH induced ovulation in all cows when the largest follicle was greater than or equal to 12 mm (16 of 16), in 17% (1 of 6) when it was 11 mm, and no ovulation when it was less than or equal to 10 mm (0 of 19). To determine the effect of LH dose on ovulatory capacity, follicular dynamics were monitored every 12 h, and cows received either 4 or 24 mg of LH when the largest follicle first achieved 10 mm in diameter (experiment 2). The proportion of cows ovulating was greater (P < 0.05) for the 24-mg (9 of 13; 69.2%) compared with the 4-mg (1 of 13; 7.7%) LH dose. To determine the effect of a higher LH dose on follicles near diameter deviation, follicular dynamics were monitored every 8 h, and cows received 40 mg of LH when the largest follicle first achieved 7.0, 8.5, or 10.0 mm (experiment 3). No cows with a follicle of 7 mm (0 of 9) or 8.5 mm (0 of 9) ovulated, compared with 80% (8 of 10) of cows with 10-mm follicles. Thus, follicles acquired ovulatory capacity at about 10 mm, corresponding to about 1 day after the start of follicular deviation, but they required a greater LH dose to induce ovulation compared with larger follicles. We speculate that acquisition of ovulatory capacity may involve an increased expression of LH receptors on granulosa cells of the dominant follicle and that this change may also be important for further growth of the dominant follicle.

Ultrasonographic and endocrine aspects of follicle deviation, and acquisition of ovulatory capacity in buffalo (Bubalus bubalis) heifers

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

Follicle deviation and ovulatory capacity in Bos indicus heifers

The objectives of Experiment I were to determine the interval from ovulation to deviation, and diameter of the dominant follicle (DF) and largest subordinate follicle (SF) at deviation in Nelore (Bos indicus) heifers by two methods (observed and calculated). Heifers (n = 12) were examined ultrasonographically every 12 h from ovulation (Day 0) to Day 5. The time of deviation and diameter of the DF and largest SF at deviation did not differ (P > 0.05) between observed and calculated methods. Overall, deviation occurred 2.5 +/- 0.2 d (mean +/- S.E.M.) after ovulation, and diameters for DF and largest SF at deviation were 6.2 +/- 0.2 and 5.9 +/- 0.2 mm, respectively. Experiment 2 was designed to determine the size at which the DF acquires ovulatory capacity in B. indicus heifers. Twenty-nine heifers were monitored every 24 h by ultrasonography, from ovulation until the DF reached diameters of 7.0-8.4 mm (n = 9), 8.5-10.0 mm (n = 10), or >10.0 mm (n = 10). At that time, heifers were treated with 25 mg of pLH and monitored by ultrasonography every 12 h for 48 h. Ovulation occurred in 3 of 9, 8 of 10, and 9 of 10 heifers, respectively (P < 0.05). In summary, there was no significant difference between observed and calculated methods of determining the beginning of follicle deviation. Deviation occurred 2.5 d after ovulation when the DF reached 6.2 mm, and ovulatory capacity was acquired by DF as small as 7.0 mm. (c) 2008 Elsevier B.V. All rights reserved.

Morphological characterization of follicle deviation in Nelore (Bos indicus) heifers and cows

Follicle diameter deviation is defined as the beginning of the differential change in growth rates between the largest and next largest follicles subsequent to wave emergence and is considered a key component of follicle selection. Follicle selection has been extensively studied in European breeds of cattle (Bos taurus) but has not been critically studied in Zebu breeds (Bos indicus). The objectives of the present study were to determine and compare the morphological characteristics of deviation associated with the first post-ovulatory wave (Wave 1) of the estrous cycle in Nelore heifers (n = 8) and nonlactating cows (n = 11). Beginning on the day of ovulation (day 0), the three largest follicles (F1-F3, respectively) were individually tracked every 12 h for 6 d using transrectal ultrasonography. In individual animals, deviation was determined graphically using visual inspection of the diameter profiles of F1, F2 and sometimes F3 (observed deviation) and mathematically using segmented regression analysis of the diameter differences between F1 and F2 or sometimes F3 (calculated deviation). Mean day of emergence of Wave 1 when F1 reached >3 rum (approximately 1 d after ovulation) and growth rate of F1 during deviation (approximately 1.4 mm/d) were not significantly different between heifers and cows. The results of determining the beginning of deviation within heifers and cows using the observed and calculated methods were not significantly different. Averaged over both methods, diameter deviation occurred 2.8 d after ovulation when F1 reached 5.7 mm in heifers, and 2.4 d after ovulation when F1 reached 6.1 mm in cows. In conclusion, the emergence of Wave 1 and growth rates and diameters of the future dominant follicles at the beginning of deviation were similar in Nelore heifers and nonlactating cows, regardless of the methods used to determine deviation. Relative to Holstein cattle, emergence of Wave 1 appeared to occur about 1 d later and diameter of the future dominant follicle at the beginning of deviation was about 2 turn smaller in Nelore. (C) 2004 Elsevier B.V. All rights reserved.

Deviation from the sech2 superradiant emission law in a two-level atomic system

The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the sech2 law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results. © 1990 The American Physical Society.