Unsuitable multiple alignment

Question

In the following MWE, I tried to have double alignment inside alignat environment. I want (x_i^4)^2 be placed under k_i^2 in the second equation. However, it seems this MWE is not correct and the output is not suitable.

\documentclass{article}
\usepackage{amsmath}

\begin{document}


\begin{alignat}{2}
&\dot{x}_i^1 = x_i^2 &&\nonumber\\
&\dot{x}_i^2 = x_i^3&&\left(k_i^2 + \frac{k_i^3}{\left(1 + 
\left(x_i^3\right)^2\right)^{\frac{1}{2}}}\left(x_i^2 - \frac{k_i^1}{\left(1 
+ \left(x_i^3\right)^2\right)^{\frac{1}{2}}}x_i^4\right)^2 + \frac{k_i^1} 
{\left(1 + x_3^2\right)^{\frac{3}{2}}}\right.\nonumber\\
&&\left.\left (x_i^4\right)^2\vphantom{\left(x_i^2 - \frac{k_i^1}{\left(1 + 
\left(x_i^3\right)^2\right)^{\frac{1}{2}}}x_i^4\right)^2}\right)\nonumber\\
&\dot{x}_i^3 = x_i^4 &&\nonumber\\
&\dot{x}_i^4 = v_i &&
\end{alignat}

\end{document}

Answer 1

You do not say what layout you want, but perhaps

\documentclass{article}
\usepackage{amsmath}

\begin{document}


\begin{equation}
\begin{aligned}
\dot{x}_i^1 &= x_i^2\\
\dot{x}_i^2 &= x_i^3\Biggl(k_i^2 + \frac{k_i^3}{(1 + 
(x_i^3)^2)^{\frac{1}{2}}}\Bigl(x_i^2 - \frac{k_i^1}{(1 
+ (x_i^3)^2)^{\frac{1}{2}}}x_i^4\Bigr)^2 + \frac{k_i^1} 
{(1 + x_3^2)^{\frac{3}{2}}}(x_i^4)^2\Biggr)\\
\dot{x}_i^3 &= x_i^4\\[\jot]
\dot{x}_i^4 &= v_i
\end{aligned}
\end{equation}

\end{document}

Note that \left\right as well as making brackets that are often too tall adds extra horizontal space which is hardly ever wanted, especially in cases like this where you need to fit an expression that is already quite long.