Animating vector on top of Bloch Sphere

Question

I have a vector a which can only move in x-y plane and has magnitude of the radius of the sphere. Is there a way to make this a animated. Animated in the sense that it rotates within the x-y plane and the angle changes accordingly.

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \draw (0,0) node[circle,fill,inner sep=1] (orig) {} -- (\r/5,-\r/3) node[circle,fill,inner sep=0.7,label=above:$\vec{a}$] (a) {};

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--phi};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}
\end{document} 

Is it possible in TikZ?

Answer 1

This is easy with this answer.

\documentclass{article}

\usepackage{animate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{animateinline}[autoplay,loop]{2}
\multiframe{21}{i=0+1}{\pgfmathsetmacro{\myangle}{-4*\i}

\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \coordinate[label=above:$\vec{a}$] (a) at (\myangle:{\r} and {\r/3});
    \coordinate (orig) at (0,0);
    \draw (orig) circle(0.1);
    \draw[-latex] (orig) -- (a);

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--a};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}}
\end{animateinline}
\end{document} 

If you want to rotate it over the full plane, use

\documentclass{article}

\usepackage{animate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{animateinline}[autoplay,loop]{2}
\multiframe{91}{i=0+1}{\pgfmathsetmacro{\myangle}{-4*\i}

\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \coordinate[label={\myangle+90}:$\vec{a}$] (a) at (\myangle:{\r} and {\r/3});
    \coordinate (orig) at (0,0);
    \draw (orig) circle(0.1);
    \draw[-latex] (orig) -- (a);

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--a};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}}
\end{animateinline}
\end{document} 

Notice that my code is for exporting the animation. If you do not want to export it, but just incorporate it in your pdf document, comment out the block

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The animation will then show on selected viewers such as acroread.