[Tex/LaTex] Align long equation after equals sign

alignequations

I see there are plenty of questions posted here with similar topics, but I can't find a solution to my question. Below is my latex code for a few equations. How can I force text on the 2nd, 3rd (and so on) lines to appear right below the equals sign? Can I also ask latex to insert a newline at the appropriate place so as to make this possible?
enter image description here

\documentclass{article}

\usepackage{amsmath}

\begin{document}

%41
\[
\begin{split}
\frac{d}{dt}\langle \Delta i_{fi1} \rangle_{1}^R = \omega\langle
\Delta i_{fi1} \rangle_{1}^I +\frac{1}{L_{fi1}}
\Big[\frac{2}{\pi}\Big\{(V_{dcL0})_{0}sin(2 \pi D_{i})\\+(\langle
\Delta v_{dcL} \rangle_{0} sin(2 \pi D_{i}))+(V_{dcL} cos(2 \pi
D_{i})2 \pi \Delta d_{i}) \Big\}-R_{fi} \langle i_{fi}
\rangle_{1}^R-\langle v_{cfi} \rangle_{1}^R \Big]
\end{split}
\]

%42 

\[
\begin{split}
\frac{d}{dt}\langle \Delta i_{fi1} \rangle_{1}^I = -\omega\langle
\Delta i_{fi1} \rangle_{1}^R +\frac{1}{L_{fi1}}
\Big[\frac{2}{\pi}\Big\{(V_{dcL0}cos(2 \pi D_{i}))+ \\(\langle \Delta
v_{dcL} \rangle_{0} cos(2 \pi D_{i}))-(V_{dcL} sin(2 \pi D_{i})2 \pi
\Delta d_{i}) \Big\}-R_{fi} \langle i_{fi} \rangle_{1}^I-\langle
v_{cfi} \rangle_{1}^I \Big]
\end{split}
\]

% 43
\[
\begin{split}
\frac{d}{dt}\langle \Delta v_{Ci}\rangle_1^IR= \omega\langle\Delta v_{Ci}\rangle_1^I +\frac{1}{C_{fi}}\Big[ \langle\Delta i_{fi1}\rangle_1^R - \frac{\langle\Delta v_{Ci}\rangle_1^R}{R_L1}\Big]
\end{split}
\]


% 44
\[
\frac{d}{dt}\langle \Delta v_{Ci} \rangle_1^I = -\omega\langle\Delta v_{Ci}\rangle_1^R +\frac{1}{C_{fi}}\Big[ \langle\Delta i_{fi1}\rangle_1^I - \frac{\langle\Delta v_{Ci}\rangle_1^I}{R_L1}\Big]
\]

% 45 
\[
\frac{d}{dt}\Big[\Delta X_{SST}\Big]=[A_{SST}][\Delta X_{SST}]+[B_{SST}][\Delta d_{SST}]
+[C_{SST}][\Delta U_{SST}]+[D_{SST}]
\]

%46 
\[
\Big[\Delta X_{SST}\Big]=\Big[X_{rectifier} | X_{DAB} | X_{inverter} \Big]$$ where
\small\small $$\  X_{rectifier} = \Big[\Delta \langle   i_{g}  \rangle  _{1}^R\hspace{0.15cm} \Delta \langle   i_{g}  \rangle  _{1}^I\hspace{0.15cm} \Delta \langle  i_{fr} \rangle  _{1}^R\hspace{0.15cm} \Delta \langle  i_{fr} \rangle  _{1}^I\hspace{0.15cm} \Delta \langle  V_{cfr} \rangle  _{1}^R\hspace{0.15cm} \Delta \langle  V_{cfr} \rangle  _{1}^I\hspace{0.15cm} \Delta \langle  V_{dcH} \rangle  _{0} \Big])\normalsize$$
$$\ X_{DAB} = \Big[\Delta \langle  i_{tp} \rangle  _{1}^R\hspace{0.3cm}   \Delta \langle  i_{tp} \rangle  _{1}^I\hspace{0.3cm}  \Delta \langle  V_{dcL} \rangle  _{0}\Big]$$ and 
$$\ X_{inverter}= \Big[\Delta \langle  i_{fi1} \rangle  _{1}^R\hspace{0.3cm} \Delta \langle  i_{fr1} \rangle  _{1}^I\hspace{0.3cm} \Delta \langle  V_{cfi1} \rangle  _{1}^R\hspace{0.3cm} \Delta \langle  V_{cfi1} \rangle  _{1}^I\Big]
\]




\[
\Big[\small \Delta d_{SST}\Big]=\Big[\Delta d_{r}\hspace{0.3cm}\Delta d_{D1}\hspace{0.3cm}\Delta d_{D2}\hspace{0.3cm}\Delta d_{i}\Big]\eqno{\hbox{(47)}}
\]

\end{document}

Best Answer

I need quit a lot a time to rearrange your MWE ... I strongly suggest you that even in editor you wrote equation on the way, that it is easy find 0 and end of lines (\\) i.e. begining of new line of equation. Beside this for trigonometric function I suggest to use \sin or \cos instead of sin and cos.

For aligning equation at some point, for example at equal sign, you should use ampersand (&).

I merge all your equations in one system. for lines, where you not like to have equation numbers, I put \notag before \\. Beside align I also use multlined environment for broke very long equations in more lines. Result is the following:

enter image description here

Code:

\documentclass{article}
    \usepackage{mathtools}

\begin{document}
%41
    \begin{align}
\frac{d}{dt}\langle \Delta i_{fi1} \rangle_{1}^R 
    & = \begin{multlined}[t]
    \omega\langle \Delta i_{fi1}\rangle_{1}^I +\frac{1}{L_{fi1}}
    \Big[\frac{2}{\pi}\Big\{(V_{dcL0})_{0}\sin(2\pi D_{i})      \\           
    +(\langle\Delta v_{dcL} \rangle_{0}\sin(2 \pi D_{i}))
    +(V_{dcL} \cos(2\pi D_{i}) 2\pi\Delta d_{i}) \Big\} -R_{fi} 
      \langle i_{fi}\rangle_{1}^R-\langle v_{cfi} \rangle_{1}^R \Big]    
      \end{multlined}                \notag \\
%42
\frac{d}{dt}\langle \Delta i_{fi1} \rangle_{1}^I 
    & = \begin{multlined}[t]
    -\omega\langle\Delta i_{fi1} \rangle_{1}^R + \frac{1}{L_{fi1}}q \\ 
        (\langle \Delta v_{dcL} \rangle_{0}\cos(2 \pi D_{i}))                
    -(V_{dcL}\sin(2 \pi D_{i})2 \pi\Delta d_{i}) \Big\}                       
        -R_{fi} \langle i_{fi} \rangle_{1}^I-\langle
        v_{cfi} \rangle_{1}^I \Big]                                
        \end{multlined}              \notag \\
% 43
\frac{d}{dt}\langle \Delta v_{Ci}\rangle_1^IR
    & = \omega\langle\Delta v_{Ci}\rangle_1^I +\frac{1}{C_{fi}}
        \Big[ \langle\Delta i_{fi1}\rangle_1^R - \frac{\langle\Delta v_{Ci}\rangle_1^R}{R_L1}\Big]                                   \notag \\
% 44
\frac{d}{dt}\langle \Delta v_{Ci} \rangle_1^I 
    & = -\omega\langle\Delta v_{Ci}\rangle_1^R +\frac{1}{C_{fi}}
        \Big[ \langle\Delta i_{fi1}\rangle_1^I - \frac{\langle\Delta v_{Ci}\rangle_1^I}{R_L1}\Big]                                   \notag \\
% 45
\frac{d}{dt}\Big[\Delta X_{SST}\Big]
    & =[A_{SST}][\Delta X_{SST}]+[B_{SST}][\Delta d_{SST}] +[C_{SST}]
        [\Delta U_{SST}]+[D_{SST}]                                      \notag \\
%46
\Big[\Delta X_{SST}\Big]
    &   =\Big[X_{rectifier} | X_{DAB} | X_{inverter}\Big]               \notag 
\intertext{where}
X_{rectifier} 
    &   = \Big[\Delta\langle i_{g} \rangle_{1}^R\hspace{0.15cm}
        \Delta\langle i_{g}  \rangle_{1}^I\
        \Delta\langle i_{fr} \rangle_{1}^R\ 
        \Delta\langle i_{fr} \rangle_{1}^I\ 
        \Delta\langle V_{cfr}\rangle_{1}^R\ 
        \Delta\langle V_{cfr}\rangle_{1}^I\
        \Delta\langle V_{dcH}\rangle_{0}\Big]                           \notag \\
X_{DAB} 
    & = \Big[\Delta\langle i_{tp} \rangle_{1}^R\
             \Delta\langle i_{tp} \rangle_{1}^I\
             \Delta\langle V_{dcL}\rangle_{0}\Big]                      \notag \\
\intertext{and}
X_{inverter}
    & = \Big[\Delta\langle i_{fi1} \rangle_{1}^R\ 
             \Delta\langle i_{fr1} \rangle_{1}^I\
             \Delta\langle V_{cfi1}\rangle_{1}^R\ 
             \Delta\langle V_{cfi1}\rangle_{1}^I\Big]                   \notag \\
%
\Big[\small \Delta d_{SST}\Big]
    & =\Big[\Delta d_{r} \ \Delta d_{D1}\
            \Delta d_{D2}\ \Delta d_{i}\Big]
    \end{align}
\end{document}

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