Abbasi Query re Summation and over-dot

$$\begin{array}{cccc}& \hfill K\left(x,y\right)& \hfill =\hfill & x^{2}y+x{y}^2\hfill \\ & \hfill & \hfill =\hfill & \sum _j^2{M}_j\left(x\right)N_j\left(y\right)\hfill \end{array}$$

$$\begin{array}{cccc}& \hfill \overrightarrow{a}& \hfill =\hfill & \overrightarrow{i}\left(r{\stackrel{·}{\omega }}_2\cos {\omega }_{2}t-r{{\omega }_2}^2\sin {\omega }_{2}t+{\stackrel{·}{\omega }}_{1}L-{{\omega }_1}^{2}r\sin {\omega }_{2}t\right)\hfill \\ & \hfill & \hfill \hfill & +\overrightarrow{j}\left(2r{\omega }_1{\omega }_2\cos {\omega }_{2}t+{\stackrel{·}{\omega }}_{1}r\sin {\omega }_{2}t-{{\omega }_1}^{2}L\right)\hfill \\ & \hfill & \hfill \hfill & +\overrightarrow{k}\left(-r{\stackrel{·}{\omega }}_2\sin {\omega }_{2}t-r{{\omega }_2}^2\cos {\omega }_{2}t\right)\hfill \end{array}$$

The GELLMU source code used for the above follows:

...

\newcommand{\omeg1}{\omega_1}

\newcommand{\omeg2}{\omega_2}

\newcommand{\dotomeg1}{{\overset{\cdot}{\omega}}_1}

\newcommand{\dotomeg2}{{\overset{\cdot}{\omega}}_2}

\newcommand{\overarrow}[1]{\overset{\rightarrow}{#1}}

...

\begin{eqnarray}[:nonum="true"]

K\bal{x, y} & = & x^2 y + x y^2 \\

\,          & = & \sum_j^2 M_j\bal{x} N_j\bal{y}\sum:

\end{eqnarray}

 

\begin{eqnarray}[:nonum="true"]

\overarrow{a} & = & 

  \overarrow{i}\bal{r\dotomeg2\func{cos}\omeg2;t

  - r\omeg2^2\func{sin}\omeg2;t + \dotomeg1;L - \omeg1^2r\func{sin}\omeg2t} \\

\, &  & + \overarrow{j}\bal{2r\omeg1\omeg2\func{cos}\omeg2;t

        + \dotomeg1;r\func{sin}\omeg2;t - \omeg1^2L} \\

\, &  & + \overarrow{k}\bal{-r\dotomeg2\func{sin}\omeg2;t

          - r\omeg2^2\func{cos}\omeg2;t}

\end{eqnarray}