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有“过满”和“未满”的警告。请帮忙，因为有很多矩阵和方程式

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有“过满”和“未满”的警告。请帮忙，因为有很多矩阵和方程式 
\documentclass[11pt]{article}

\begin{document}


The above equations on application of Laplace Transform become: 
$$sL_1\hat{i}_{L1}(s) = D\cdot \hat{v}_{C1}(s) + D\cdot \hat{v}_{C2}(s) - D\prime \cdot \hat{v}_g(s) + (C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)$$ $$sL_2\hat{i}_{L2}(s) = -D\prime \cdot \hat{v}_{C1}(s) + D\cdot \hat{v}+{C2}(s) + D\prime \cdot \hat{v}_g(s) + (C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)$$ $$sC_1\hat{v}_{C1}(s) = -D\cdot \hat{i}_{L1}(s)+ D\prime \cdot \hat{i}_{L2}(s) + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D\prime \cdot \hat{i}_l(s)$$ $$sC_1\hat{v}_{C1}(s) = D\prime \cdot \hat{i}_{L1}(s)- D\cdot \hat{i}_{L2}(s) + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D\prime \cdot \hat{i}_l(s)$$ $$sL_l\hat{i}_l(s) = D\prime \cdot \hat{c}_{C1}(s) + D\prime \cot \hat{v}_{C2}(s) - D\prime \cdot \hat{v}_g(s) +(V_g - V_D - V_{C1} - V_{C2})\cdot \hat{d}(s) - R_l \cdot \hat{i}_l(s)$$

\end{document}

错误：

181
Underfull \hbox (badness 10000) in paragraph at lines 181--181
181
Overfull \hbox (22.63293pt too wide) detected at line 181

答案1

$$根本不要在 LaTeX 中使用，（LaTeX 语法是\[），但也不要一个接一个地使用显示数学环境，而是使用多行显示，例如align。

也使用'not\prime来获取上标素数。

在此处输入图片描述

\documentclass[11pt]{article}

\usepackage{amsmath}

\begin{document}


The above equations on application of Laplace Transform become: 
\begin{align*}
sL_1\hat{i}_{L1}(s) &=
\begin{aligned}[t]
 D\cdot \hat{v}_{C1}(s) + D\cdot \hat{v}_{C2}(s) - D' \cdot \hat{v}_g(s) + {}\\
(C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)
\end{aligned}\\
sL_2\hat{i}_{L2}(s) &= 
\begin{aligned}[t]
-D' \cdot \hat{v}_{C1}(s) + D\cdot \hat{v}+{C2}(s) + D' \cdot \hat{v}_g(s) + {}\\
(C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)
\end{aligned}\\
sC_1\hat{v}_{C1}(s) &= -D\cdot \hat{i}_{L1}(s)+ D' \cdot \hat{i}_{L2}(s) + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D' \cdot \hat{i}_l(s)\\
sC_1\hat{v}_{C1}(s) &= D' \cdot \hat{i}_{L1}(s)- D\cdot \hat{i}_{L2}(s) + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D' \cdot \hat{i}_l(s)\\
sL_l\hat{i}_l(s) &= 
\begin{aligned}[t]D' \cdot \hat{c}_{C1}(s) + D' \cot \hat{v}_{C2}(s) - D' \cdot \hat{v}_g(s) +{}\\
(V_g - V_D - V_{C1} - V_{C2})\cdot \hat{d}(s) - R_l \cdot \hat{i}_l(s)
\end{aligned}
\end{align*}

\end{document}

一种可能的变体，其中所有方程都被拆分以使宽度尽可能小；为了更好地区分各个方程，在它们之间添加了一些垂直空间。

\documentclass[11pt]{article}
\usepackage{amsmath}

\begin{document}

The above equations on application of Laplace Transform become
\begin{align*}
sL_1\hat{i}_{L1}(s) &=
  \!\begin{aligned}[t]
    &D\cdot \hat{v}_{C1}(s) + D\cdot \hat{v}_{C2}(s) - D' \cdot \hat{v}_g(s) \\
    &\qquad + (C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)
  \end{aligned}
\\[1\jot]
sL_2\hat{i}_{L2}(s) &=
  \!\begin{aligned}[t]
    &{-}D' \cdot \hat{v}_{C1}(s) + D\cdot \hat{v}+{C2}(s) + D' \cdot \hat{v}_g(s) \\
    &\qquad + (C_{C1} + V_{C2} - V_g + V_D)\cdot \hat{d}(s)
  \end{aligned}
\\[1\jot]
sC_1\hat{v}_{C1}(s) &=
  \!\begin{aligned}[t]
    &{-}D\cdot \hat{i}_{L1}(s)+ D' \cdot \hat{i}_{L2}(s) \\
    &\qquad + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D' \cdot \hat{i}_l(s)
  \end{aligned}
\\[1\jot]
sC_1\hat{v}_{C1}(s) &=
  \!\begin{aligned}[t]
    &D' \cdot \hat{i}_{L1}(s)- D\cdot \hat{i}_{L2}(s) \\
    &\qquad + (-I_{L1} -I_{L2} - I_1)\cdot \hat{d}(s) -D' \cdot \hat{i}_l(s)
  \end{aligned}
\\[1\jot]
sL_l\hat{i}_l(s) &=
  \!\begin{aligned}[t]
    &D' \cdot \hat{c}_{C1}(s) + D' \cot \hat{v}_{C2}(s) - D' \cdot \hat{v}_g(s) \\
    &\qquad  +(V_g - V_D - V_{C1} - V_{C2})\cdot \hat{d}(s) - R_l \cdot \hat{i}_l(s)
  \end{aligned}
\end{align*}

\end{document}

在此处输入图片描述

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