## 4 Numerical Experiments
### Experiment 1, \(n=1\)
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{L_{1}}_{\text{initial [m]}}\) & \(\mathbf{L_{1}}_{\text{calculated [m]}}\) & \(\overline{\text{error}}(\mathbf{\omega_{1}})\) \\ \hline \(1.0000\times 10^{-5}\) & \(4.9997\times 10^{-5}\) & \(2.0102\times 10^{-5}\) \\ \hline \(1.4211\times 10^{-5}\) & \(4.9999\times 10^{-5}\) & \(0.4557\times 10^{-5}\) \\ \hline \(1.8421\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0763\times 10^{-5}\) \\ \hline \(2.2632\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0070\times 10^{-5}\) \\ \hline \(2.6842\times 10^{-5}\) & \(4.9998\times 10^{-5}\) & \(7.2456\times 10^{-5}\) \\ \hline \(3.1053\times 10^{-5}\) & \(4.9998\times 10^{-5}\) & \(1.6766\times 10^{-5}\) \\ \hline \(3.5263\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.2480\times 10^{-5}\) \\ \hline \(3.9474\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0143\times 10^{-5}\) \\ \hline \(4.3684\times 10^{-5}\) & \(4.9994\times 10^{-5}\) & \(4.2977\times 10^{-5}\) \\ \hline \(4.7895\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0465\times 10^{-5}\) \\ \hline \(5.2105\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0533\times 10^{-5}\) \\ \hline \(5.6316\times 10^{-5}\) & \(4.9992\times 10^{-5}\) & \(5.7583\times 10^{-5}\) \\ \hline \(6.0526\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0444\times 10^{-5}\) \\ \hline \(6.4737\times 10^{-5}\) & \(4.9999\times 10^{-5}\) & \(0.9854\times 10^{-5}\) \\ \hline \(6.8947\times 10^{-5}\) & \(4.9987\times 10^{-5}\) & \(9.5397\times 10^{-5}\) \\ \hline \(7.3158\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0695\times 10^{-5}\) \\ \hline \(7.7368\times 10^{-5}\) & \(4.9998\times 10^{-5}\) & \(1.7327\times 10^{-5}\) \\ \hline \(8.1579\times 10^{-5}\) & \(4.9996\times 10^{-5}\) & \(2.7074\times 10^{-5}\) \\ \hline \(8.5789\times 10^{-5}\) & \(4.9997\times 10^{-5}\) & \(2.4424\times 10^{-5}\) \\ \hline \(9.0000\times 10^{-5}\) & \(4.9999\times 10^{-5}\) & \(0.8905\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results for case (1.1.3). \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{L_{1}}_{\text{initial [m]}}\) & \(\mathbf{L_{1}}_{\text{calculated [m]}}\) & \(\overline{\text{error}}(\mathbf{\omega_{1}},\mathbf{\omega_{2}})\) \\ \hline \(1.0000\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0114\times 10^{-5}\) \\ \hline \(1.4211\times 10^{-5}\) & \(5.0001\times 10^{-5}\) & \(0.7609\times 10^{-5}\) \\ \hline \(1.8421\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0022\times 10^{-5}\) \\ \hline \(2.2632\times 10^{-5}\) & \(5.0001\times 10^{-5}\) & \(6.7586\times 10^{-5}\) \\ \hline \(1.1306\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.1085\times 10^{-5}\) \\ \hline \(3.1053\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0001\times 10^{-5}\) \\ \hline \(3.5263\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.2329\times 10^{-5}\) \\ \hline \(3.9474\times 10^{-5}\) & \(5.0001\times 10^{-5}\) & \(0.7588\times 10^{-5}\) \\ \hline \(4.3684\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.1635\times 10^{-5}\) \\ \hline \(4.7895\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.003\times 10^{-5}\) \\ \hline \(3.1053\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0003\times 10^{-5}\) \\ \hline \(5.6316\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0072\times 10^{-5}\) \\ \hline \(6.0526\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.2296\times 10^{-5}\) \\ \hline \(6.4737\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.1868\times 10^{-5}\) \\ \hline \(6.8947\times 10^{-5}\) & \(5.0000\times 10^{-5}\) & \(0.0174\times 10^{-5}\) \\ \hline \(7.3158\times 10^{-5}\) & \(5.0002\times 10^{-5}\) & \(2.2731\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results for case (1.1.4).