## 4 Results
### Systematic Verification of the ADCS
#### 4.2.1 Source Code Verification and Performance Simulation
The attitude stability of the CubeSat is affected by this range of angular velocity, determining how the CubeSat responds to external disturbances; this range also influences the response and performance of the ADCS in maintaining a stable attitude under different angular velocities. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Angular Velocity** & **Inertia Matrix** \\ \hline \multirow{3}{*}{Initial value} & x y z & Ixx Iyy Izz \\  & \(-0.001\quad 0.003\quad 0.002\) & 1.6X10-17 1.3X10-17 1.4X10-17 \\ Final value & 0.004 0.008 0.007 & 1X10-7 1X10-7 1X10-7 \\ Mean & 0.003 0.001 0.001 & 1X10-7 1X10-7 1X10-7 \\ Sampling method & Random & Random \\ Distribution & Uniform & Uniform \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter sensitivity analysis, Monte Carlo/angular velocity/inertia matrix. Figure 13: Mean of pointing accuracy with Monte Carlo simulation. Angular velocity, initial orbit condition, Euler initial rotation, \(I_{B}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Initial Cubesat Orbit Condition** & **Euler Angles** \\ \hline \multirow{3}{*}{Initial value} & \(\theta\) & x y z \\  & 0 & 45 \(-\)45 45 \\ Final value & 360 & 360 360 360 \\ Mean & 0.1 & 0.1 0.2 0.3 \\ Sampling method & Random & Random \\ Distribution & Uniform & Uniform \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter sensitivity analysis, Monte Carlo/Initial CubeSat orbit condition/Euler angles). Otherwise, CubeSat's inertia matrix was approximated using Solidworks, obtaining the following:  
\[[I_{\text{B}}]= \begin{bmatrix}1556542.74&18844.31&-25.84\\ 18844.31&1337462.20&-2447.28\\ -25.84&-2447.28&1408210.65\end{bmatrix} \times 10^{-9}[\text{Kg}\cdot\text{m}^{2}]\]  
So, variation in the inertia matrix is depicted in Figure 16; depicted on the x-axis is the offset value that is added to the moments of inertia (the diagonal of the inertia matrix \(\mathbf{I}_{\mathcal{XX}}\), \(\mathbf{I}_{\mathcal{YY}}\), \(\mathbf{I}_{\mathcal{ZZ}}\)). Hence, the variation in the inertia matrix is in the range of \((1\times 10^{-3}\leq variation\leq 5\times 10^{-3})\), applied to the initial moment of inertia: \(\mathbf{I}_{\mathcal{XX}}= \begin{bmatrix}1.556\times 10^{-15}\end{bmatrix} \); \(\mathbf{I}_{\mathcal{YY}}= \begin{bmatrix}1.337\times 10^{-15}\end{bmatrix} \); \(\mathbf{I}_{\mathcal{ZZ}}= \begin{bmatrix}1.408\times 10^{-15}\end{bmatrix} \). This variation was carried out to analyze the possible disturbances and variations within the construction and manufacturing process of the CubeSat, or the degradation of the CubeSat structure over time, resulting in a variation in control performance. The initial 3-1-3 Euler angles regarding the initial frame \([BN](0)\) suffer a variation in each axis in a range of \((0\leq degrees\leq 360)\) trying to cover all possible rotations; the initial pointing error for each normal resultant of the Euler vector is depicted in Figure 17; in this way it is possible to observe the performance of ADCS with respect to the change in initial rotation verifying the mean of the pointing error depicted on the y-axis. Afterward, the variation in the perigee argument in orbit elements is depicted in Figure 18. So, the range of perigee (\(\mathbf{\omega}\)) is \((0\leq perigeeargument\leq 360)\) degrees in the Monte Carlo simulation; the inclination and ascending node remain constants to obtain a circular orbit; the values of the ascending node and inclination for an optimal orbit that crosses Bolivian territory are \([\mathbf{16;30;\omega}]\), respectively.