## 5 System Modeling and Simulation  
### System Modeling of Capture Condition  
The capture task of EASIST can be divided into longitudinal and lateral capture, which are undertaken by EMPU and ERSD, respectively. Taking EMPU as an example, according to the power bond graph theory, the energy transfer of the transmission system can be described as the following process: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Symbol** & **Value** & **Parameters** & **Symbol** & **Value** \\ \hline Distance between the mass center and the \(Z\)-axis & \(L_{\rm H}\) & 0.9 m & Helicopter mass & \(M_{\rm H}\) & 10,000 kg \\ \hline Distance between the force point and the \(Z\)-axis & \(L_{\rm E}\) & 0.9 m & \begin{tabular}{c} Distance between the front wheel and rear wheel centerline \\ \end{tabular} & \(L\) & 7 m \\ \hline Distance between the two rear wheels & \(B\) & 3.5 m & \begin{tabular}{c} Height from the mass center to the deck \\ \end{tabular} & \(H\) & 2 m \\ \hline Distance from the wind center to the \(Z\)-axis & \(L_{\rm W}\) & 0.9 m & \begin{tabular}{c} Height from the wind center to the deck \\ \end{tabular} & \(H_{\rm W}\) & 1.3 m \\ \hline Lateral wind action constant & \(A_{\rm X}C_{\rm W}\) & 20 & \
\begin{tabular}{c} Longitudinal wind force \\ action constant \\ \end{tabular} & \(A_{\rm Y}C_{\rm W}\) & 2.5 \\ \hline Air density & \(\rho\) & 1.29 kg/m\({}^{3}\) & Rolling friction coefficient & \(f\) & 0.02 \\ \hline Maximum roll angle & \(\theta\) & \(10^{\circ}\) & Maximum pitch angle & \(\lambda\) & 2.5\({}^{\circ}\) \\ \hline Maximum lateral acceleration & \(a_{\rm x}\) & \(1\,\rm m/s^{2}\) &
\begin{tabular}{c} Maximum \\ longitudinal acceleration \\ \end{tabular} & \(a_{\rm y}\) & \(1\,\rm m/s^{2}\) \\ \hline Maximum vertical acceleration & \(a_{\rm z}\) & \(0.5\,\rm m/s^{2}\) & Maximum wind speed & \(v_{\rm W}\) & 12 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the helicopter and deck. 1. The driving torque of the asynchronous motor (Potential Source) drives the reducer to rotate (Inertia Element and Resistive Element). 2. The reducer (Converter) drives the steel cable reel to rotate (Inertia Element and Resistive Element). 3. The steel cable reel transforms rotational motion to straight motion by the steel cable (Converter) and the chain (Converter). 4. The steel cable (Inertia Element and Resistive Element) drives ERSD and power cable (Inertia Element and Resistive Element) to move quickly. In contrast, the chain (Inertia Element and Resistive Element) drives the power cable reel to rotate (Converter, Inertia Element, and Resistive Element). 5. The chain and steel cable length varies with the tensile force (Capacitive Element). The power bond graph model of the longitudinal capture system can be built according to the above descriptions, as shown in Figure 14, and the related bond graph was augmented and simplified. Similarly, the bond graph model of the lateral capture system can be obtained, as shown in Figure 15.  
For EMPU, take the state equation as follows:  
\[X_{1}^{\prime}=A_{1}\cdot X_{1}+B_{1}\cdot U_{1}. \tag{23}\]  
The generalized momentum \(p_{2}\), \(p_{16}\), \(p_{25}\), and generalized displacement \(q_{14}\), \(q_{22}\) corresponding to \(l_{2}\), \(l_{16}\), \(l_{25}\), \(C_{14}\), \(C_{22}\) are selected as the state variables of the system, which is shown as follows:  
\[X_{1}=\big{[} \begin{array}{cccc}p_{2}&q_{14}&p_{16}&q_{22}&p_{25}\end{array}  \big{]}^{\text{T}}. \tag{24}\]  
The input of the system is the output torque of the motor, which is shown as follows:  
\[U_{1}=[Se_{1}]. \tag{25}\]  
Figure 14: The bond graph of the longitudinal capture system. Figure 15: The bond graph of the lateral capture system. The characteristic equation of Resistive Element \(R_{3}\), \(R_{7}\), \(R_{12}\), \(R_{17}\), \(R_{20}\), and \(R_{26}\) is shown as follows:  
\[\left\{