\documentclass[12pt, a4paper,fleqn]{report}
\doublespacing
\usepackage[comma,super,sort&compress]{natbib}
\bibliographystyle{rsc.bst}
\usepackage{comment}
\setcounter{secnumdepth}{4}
\usepackage{graphicx}
\usepackage{amsmath}
\graphicspath{ {images/} }
\begin{document}
\section{Molecular dynamics simulations}
....content....
\begin{equation}
\centering
m_\mathit{i} \frac{\delta^2\mathbf{r_\mathit{i}}}{\delta \mathit{t}^2}= \mathbf{F_\mathit{i}},\mathit{i} = 1....N.
\end{equation}
[Tex/LaTex] Center an equation
alignequations
Related Solutions
You could try:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{array}[t]{c @{\,} c @{{}={}} c}
AAAAAA & yyyyy & bbbbbb \\
A & y & b \\
\end{array}
\end{equation}
\end{document}
Addendum, to address the OP's follow-up query: To typeset the two versions of the matrix equation you've added to your initial query, I would use nearly the same code as given above, with the exception that I would replace @{\,} with @{} as the separator between the first and second column of the array. This is because, in my not-so-humble opinion..., the spacing between matrix-like environment provided by the amsmath package (which provides the pmatrix environments) is a bit excessive, especially so for the case at hand. (If you do want the default spacing of the amsmath package, just keep the @{\,} inter-column specification as per the initial answer.)
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{array}[t]{c @{} c @{{}={}} c}
\begin{pmatrix}
1 & 0 \\
0 & 1 \\
0 & 0 \\
\end{pmatrix} &
\begin{pmatrix}
x\\
y\\
\end{pmatrix} &
\begin{pmatrix}
x\\
y \\
0\\
\end{pmatrix} \\[4ex]
A & x & d\\
\end{array}
\end{equation}
\end{document}
You can lower manually the clause:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\label{eq:distrib}
\begin{alignedat}{2}
n_c &= \max[N \cdot z_{\max} \cdot x, 2 \cdot n_{\min}]
&\quad&\raisebox{-.5\normalbaselineskip}[0pt][0pt]{%
where $x\sim U([0,1])$%
} \\
n_{co} &= \min[\max[n_c \cdot x, n_{\min}], n_c - n_{\min}] \\
n_{cp} &= n_c - n_{co} \\
n_f &= N - n_c
\end{alignedat}
\end{equation}
\end{document}
I used \max and \min (you should, too). I also removed all \left and \right tokens, which only do evil here.
I'd also suppress all \cdot symbols, which are very seldom used to denote multiplication in professional math.
However, my feeling is that the clause about x should be moved in the text following the display.
Best Answer
The
fleqnclass option causes equations to be left-aligned (you specifically ask for this feature). Removing it restores the default behavior: centered alignment.