# Transient Attitude Motion of TNS-0#2 Nanosatellite during Atmosphere Re-Entry
## 4 Measurements Processing Results and Passive Attitude Motion Regimes Analysis  
### Attitude Stabilization After The Launch  
The first communication session that included the sensors measurements telemetry occurred on 19 August at 17 h 11 min UTC. Figure 3 shows the measurements of the magnetometer.  
Figure 3: The first measurements from the magnetometer.  
Magnetometer measurements include the permanent magnet and hysteresis rods influence. The main contribution is due to the magnet. The corresponding constant bias in the magnetometer measurements was estimated using the least squares method. The technique involves the functional of the difference between the field magnitudes according to the measurements and according to the IGRF model. Figure 4 shows the obtained geomagnetic field corrected for the constant bias of the magnetometer measurements \(\textbf{B}_{bias}=\left[\begin{array}{cccc}5.8&-90.8&-20.9&\cdot 10^{3}\, \text{nT}.\end{array}\right.\)  
Figure 5 depicts the measured and predicted unit geomagnetic induction vector according to the motion reconstruction scheme discussed in previous section. The magnetometer measurements and their predicted magnitudes are close. This indicates relatively accurate satellite attitude reconstruction.  
Figure 6 shows the angular velocity reconstructed according to the found initial conditions and the equations of motion. Note that the aerodynamic torque is not taken into account for the motion after the launch. The initial orbit altitude is about 420 km and the aerodynamic torque small and can be neglected.  
Figure 4: Measured geomagnetic field excluding bias.  
Figure 5: Measured and predicted unit vector of the geomagnetic field.  
Measurements from the Sun sensors were predicted and compared with actual measurements. It is assumed that the photodiode sensors have a sensitive area in the form of a cone with an opening angle of 120 degrees. The sensor measurements within this region are considered to have a cosine-like dependence on the incidence angle. The measurements are zero outside this region. The measurements were normalized by the maximum value according to the procedure described in [17]. Figure 7 presents a comparison of sensor measurements and their predicted values using the satellite motion model with initial conditions obtained from the magnetometer data. There is some correlation between the corresponding curves. Periodic significant discrepancy is due to the unaccounted influence of the Earth's albedo. Its contribution can reach up to 30% of the Sun's influence. In particular, non-zero measurements from Sun sensors No. 4 and 5 can be explained by the effect of the light reflected from the Earth. These sensors are located at opposite sides of the satellite. This indicates the clearly low accuracy of the Sun sensors. Therefore, they are not used directly in the attitude reconstruction process. Their measurements are utilized only to validate the results of the reconstruction with the magnetometer measurements.  
Figure 8 shows the time history of the angular velocity magnitude after the launch of the satellite. The curve is close to linear, which corresponds to the model of the hysteresis dampers. The damping finished and the satellite achieved the required magnetic attitude after about 36 days. This is due to a very high initial angular velocity of about 79 deg./s.  
Figure 6: Angular velocity components.  
Figure 7: Sun sensors normalized measurements and its predicted values.