List_of_symbols.tex

% LIST OF SYMBOLS
% Write out the List of Symbols in this page

\chapter*{List of Symbols}
\label{ch:List_of_symbols}
Here the list of the symbols adopted.

\begin{table}[h]
    \centering
    \caption{List of Symbols used throughout the thesis.}
    \renewcommand{\arraystretch}{1.5} % Increase the vertical spacing between rows
    \begin{tabular}{@{}l@{\hspace{3cm}}l@{}}
    \toprule
    \textbf{Symbols} & \textbf{Description} \\
    \midrule
    ${A,B}$  & coordinate frames \\
    ${\mathbf{p}}$ & arbitrary point \\
    ${\mathbf{o}_B}$  & origin of $B$ \\
    ${[A]}$ & orientation frame associated to [A] \\
    ${B[A]}$  & frame with origin $\mathbf{o}_B$ and orientation $A$ \\
    ${{}^{A}\mathbf{p}}$ & coordinates of $\mathbf{p}$ w.r.t. $A$ \\
    ${{}^{A}\mathbf{o}_B}$  & coordinates of $\mathbf{o}_B$ w.r.t. $A$ \\
    ${{}^{A} H_B}$  & homogeneous transformation from $B$ to $A$ \\
    ${{}^{A} X_B}$  & velocity transformation from $B$ to $A$ \\
    ${}^{C} \mathbf{v}_{A,B}$  & 6D velocity expressing the velocity of $B$ w.r.t. A written in $C$ \\
    ${}^{C} \mathbf{v}^{\wedge{}}_{A,B}$  & 4 x 4 matrix representation of ${}^{C} \mathbf{v}_{A,B}$  \\
    ${}^{C} \mathbf{v}_{A,B}\times$  & 6 x 6 matrix representation of the 6D velocity cross product  \\
    ${}^{C}J_{A,B}$  & Jacobian relating the velocity of $B$ w.r.t. $A$ expressed in C \\
    ${}^{C}J_{A,B/F}$  & Jacobian relating the velocity of $B$ w.r.t. $A$ expressed in $C$, \\ & where the moving-base velocity is expressed in $F$ \\
     \bottomrule
    \end{tabular}
\end{table}