4、线性系统分析：从基础理论到实际应用

线性系统分析：从基础理论到实际应用

1. 线性系统基础

在研究线性系统时，我们会遇到一些关键的参数和方程。首先，有如下几个重要的表达式：
- (a_{31} = \frac{v_g}{r} \sin \theta_d \sec^2 \delta_d + \frac{\Omega^2 r}{v_g} \sin \theta_d \cos 2\delta_d + 2\Omega \cos \delta_d)
- (a_{33} = \tan \delta_d \left(\frac{v_g \cos \theta_d + \frac{\partial v_g}{\partial \theta_d} \sin \theta_d}{r}\right) - u_d \left(\frac{1}{v_g^2} \frac{\partial v_g}{\partial \theta_d} + \frac{\Omega^2 r}{2} \frac{\sin 2\delta_d}{\cos \theta_d}\right) - \frac{\sin \theta_d}{v_g^2} \frac{\partial v}{\partial \theta_d})
- (v_g = \sqrt{v^2 - v_w^2 \sin^2(\psi_w - \theta_d) - v_w \cos(\psi_w - \theta_d)})
- (\frac{\partial v_g}{\partial \theta_d} = \left(1 - \frac{v_w \cos(\psi_w - \theta_d)}{\sqrt{v^2 - v_w^2 \sin^2(\psi_w - \theta_d)}}\righ