记忆

注意：图床已经不公开，导致图片无法正常显示。

电路

$$\begin{array}{c|c|c|c|c} \hline & r 参数 & g 参数 & h 参数 & a 参数 \\ \hline \\ R_{\mathrm{i}} & \frac{r_{11} R_{\mathrm{L}}+\Delta_r}{r_{22}+R_{\mathrm{L}}} & \frac{g_{22}+G_{\mathrm{L}}}{g_{11} G_{\mathrm{L}}+\Delta_g} & \frac{h_{11} G_{\mathrm{L}}+\Delta_h}{h_{22}+G_{\mathrm{L}}} & \frac{a_{11} R_{\mathrm{L}}+a_{12}}{a_{21} R_{\mathrm{L}}+a_{22}} \\ \\ \hline \\ R_0 & \frac{r_{22} R_{\mathrm{S}}+\Delta_r}{r_{11}+R_{\mathrm{S}}} & \frac{g_{11}+G_{\mathrm{S}}}{g_{22} G_{\mathrm{S}}+\Delta_g} & \frac{h_{11}+R_{\mathrm{S}}}{h_{22} R_{\mathrm{S}}+\Delta_h} & \frac{a_{22} R_{\mathrm{S}}+a_{12}}{a_{21} R_{\mathrm{S}}+a_{11}} \\ \\ \hline \\ u_{oc} & \frac{r_{21}}{r_{11}+R_{\mathrm{S}}} u_{\mathrm{S}} & -\frac{g_{21}}{g_{22}+\Delta_g R_{\mathrm{5}}} u_{\mathrm{S}} & -\frac{h_{21}}{h_{22} R_{\mathrm{S}}+\Delta_h} u_{\mathrm{S}} & \frac{1}{a_{11}+a_{21} R_{\mathrm{S}}} u_{\mathrm{S}} \\ \\ \hline \\ A_u & \frac{r_{21} R_{\mathrm{L}}}{r_{11} R_{\mathrm{L}}+\Delta_r} & -\frac{g_{21}}{g_{22}+G_{\mathrm{L}}} & -\frac{h_{21} R_{\mathrm{L}}}{h_{11}+R_{\mathrm{L}} \Delta_h} & \frac{R_{\mathrm{L}}}{a_{12}+a_{11} R_{\mathrm{L}}} \\ \\ \hline \\ A_i & -\frac{r_{21}}{r_{22}+R_{\mathrm{L}}} & \frac{g_{21} G_{\mathrm{L}}}{g_{11} G_{\mathrm{L}}+\Delta_g} & \frac{h_{21} G_{\mathrm{L}}}{h_{22}+G_{\mathrm{L}}} & -\frac{1}{a_{22}+a_{21} R_{\mathrm{L}}} \\ \\ \hline \end{array}$$

端接

大物

理力

1. 常见的转动惯量（图床不公开了）

数理

$$\begin{array}{c} F\lbrack a_{1}f_{1}(x)+a_{2}f_{2}(x)\rbrack=a_{1}F\lbrack f_{1}(x)\rbrack+a_{2}F\lbrack f_{2}(x)\rbrack &线性定理 \\ F[f(x-x_{0})]=e^{-i k x_{0}}F[f(x)] &延迟定理 \\F[f(x-x_{0})]=\int_{-\infty}^{\infty}f(x-x_{0})e^{-i k x}d x \\= \int_{\infty}^{\infty}\!f(x-x_{0}){\color {red} e^{-i k(x-x_{0})}e^{-i k x_{0}}}d x \\=e^{-i k x_{0}}\int_{-\infty}^{\infty}\!f(x)e^{-i k x}d x \\ F[f(x)e^{i k_{0}x}]=c(k-k_0),~~~c(k)\equiv F[f(x)] & 位移定理 \\ F[f(x)e^{i k_{0}x}]=\int_{-\infty}^{\infty}f(x)e^{i k_{0}x}e^{-i k x}d x \\=\int_{-\infty}^{\infty}\!f(x)e^{-i(k-k_{0})x}d x \\ F\left[f^{\prime}(x)\right]=i k F[f(x)], \quad F\left[f^{(n)}(x)\right]=(i k)^{n} F[f(x)] & 微分定理 \\F\left[f^{\prime}(x)\right]=\int_{-\infty}^{\infty} f^{\prime}(x) e^{-i k x} d x \\=\left.f(x) e^{-i k x}\right|_{-\infty} ^{\infty}+i k \int_{-\infty}^{\infty} f(x) e^{-i k x} d x 【分部积分】 \\F\left[f_{1}(x)\right] \cdot F\left[f_{2}(x)\right]=F\left[f_{1}(x) * f_{2}(x)\right] &卷积定理 \\ f_{1}(x) * f_{2}(x)=\int_{-\infty}^{\infty} f_{1}(x-\xi) f_{2}(\xi) d \xi \\ F\left[f_{1}(x) * f_{2}(x)\right]=\int_{-\infty}^{\infty}\left[\int_{-\infty}^{\infty} f_{1}(x-\xi) e^{-i k x} d x\right] f_{2}(\xi) d \xi \\=F\left[f_{1}(x)\right] \int_{-\infty}^{\infty} f_{2}(\xi) e^{-i k \xi} d \xi \\ F[f(a x)]=\frac{1}{|a|} c\left(\frac{k}{a}\right), \quad a \neq 0 &坐标缩放定理 \end{array}$$