热力耦合模型（Thermo-mechanical Coupling Model）

$$\rho_{He} = \frac{p_{He} M_{He}}{RT_{He}}$$

$$\frac{\partial \rho_{He}}{\partial T_{He}} = -\frac{p_{He} M_{He}}{RT_{He}^2}$$

$$B = (\rho_{air} - \rho_{He}) V_{He} g$$

$$\dot{B} = -\frac{\partial \rho_{He}}{\partial T_{He}} \dot{T}_{He} \cdot V_{He} g$$

$$\Delta p = p_{He} - p_{ext}$$

$$V_{He} = V_{envelope} - V_{ballonet}$$

$$\begin{bmatrix} C_{skin} & 0 \\ 0 & C_{He} \end{bmatrix} \begin{bmatrix} \dot{T}_{skin} \\ \dot{T}_{He} \end{bmatrix} = \begin{bmatrix} Q_{ext} \\ Q_{int} \end{bmatrix} - \mathbf{H} \begin{bmatrix} T_{skin} \\ T_{He} \end{bmatrix}$$

$$m\begin{bmatrix} \dot{u} \\ \dot{v} \\ \dot{w} \end{bmatrix} = \begin{bmatrix} X \\ Y \\ Z \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \\ B - mg \end{bmatrix}$$

$$\frac{\partial B}{\partial T_{He}} = -\frac{p_{He} M_{He}}{RT_{He}^2} V_{He} g$$