3D rotation for portion of tikz

Question

I'm trying to reproduce the Euler angles diagram, here is the first first rotation known as precession rotation

And I was successful reproducing this diagram in TikZ+pdfLaTeX

Here is the code for this portion

\documentclass[12pt]{book}

\usepackage[top = 1in,
            bottom = 1in,
            left = 0.75in,
            right = 0.75in
            ]{geometry}
\usepackage{tikz}
\usetikzlibrary{3d}

\usepackage{graphicx}
\usepackage{amsmath, amsfonts}
\usepackage{wrapfig}
\usepackage{pgfplots}
\begin{tikzpicture}[scale = 3]

\begin{document}

\begin{scope}[canvas is zx plane at y=0]

\draw [ultra thin, step = 0.25, lightgray](-1, -1) grid (1, 1);

\filldraw [fill = orange!20, draw = orange] (0, 0) -- (0.5, 0) arc [start angle = 0, end angle = 45, radius = 0.5] (0.71, 0.71) -- cycle;

\filldraw [fill = orange!20, draw = orange] (0, 0) -- (0, 0.5) arc [start angle = 90, end angle = 135, radius = 0.5] (-0.71, 0.71) -- cycle;
\draw [->, orange, ultra thick](0, 0) -- (1, 0);
\draw [->, orange, ultra thick](0, 0) -- (0, 1);
\draw [->, red, ultra thick] (0, 0) -- (0.71, 0.71);
\draw [->, red, ultra thick] (0, 0) -- (-0.71,
 0.71);

\node [anchor = north west] at (0, 1) {$\vec{i}$};
\node [anchor = north] at (1, 0) {$\vec{j}$};

\draw [green, ultra thick](0, 0) circle (1);

\end{scope}

\draw [->, orange, ultra thick] (0, 0, 0) -- (0, 1, 0);

\begin{scope}[canvas is zx plane at y=0.5]

\draw [->, blue](0, -0.15) arc [start angle = -90, end angle = 180, radius = 0.15];

\node [anchor = south west] at (0, 0.2) {$\dot{\Psi}\vec{z_0}$};

\end{scope}

\node [anchor = south east] at (0, 1, 0) {$\vec{z_0}$};
\end{tikzpicture}
\end{document}

Now what I want to do is to rotate this tikzpicture as the rotation in the picture (some modifications are tolerated)

I tried to hard, I found other people who had done an amazing rotation, like the box rotation at texample

your help is appreciated, and in case it is important, I'm using book as a document class, running MikTeX.

Answer 1

You can achieve that with the options rotate around x, rotate around y, rotate around z which allows you to rotate the coordinate system around one of the current axes.

Something like this:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{3d}

\begin{document}
\begin{tikzpicture}[scale=3,line cap=round]
\begin{scope}[rotate around y=45,rotate around z=30,canvas is zx plane at y=0]
  \draw [green!50!black, dashed, ultra thick] (-1,0) arc (180:360:1);
\end{scope}

\begin{scope}[canvas is zx plane at y=0]
  \draw [ultra thin, step = 0.25, lightgray] (-1,-1) grid (1,1);
  \draw [dashed, red] (225:1) -- (0,0) -- (135:1);
  \draw [green, ultra thick] (0, 0) circle (1);
  \foreach\i in{0,90}
  {
    \filldraw [fill= orange!20, draw = orange] (0,0) -- (\i:0.5) arc (\i:\i+45:0.5) -- cycle;
    \draw [->, orange, ultra thick] (0,0) -- (\i:1);
  }
  \node [anchor = north west] at (0, 1) {$\vec{i}$};
  \node [anchor = north]      at (1, 0) {$\vec{j}$};
\end{scope}

\begin{scope}[rotate around y=45,rotate around z=30]
  \draw [canvas is zx plane at y=0, green!50!black, ultra thick] (1, 0) arc (0:180:1);
  \foreach\i in {0,90}
    \filldraw [canvas is xy plane at z=0, fill=red!20, draw=red] (0,0) -- (\i-30:0.4) arc (\i-30:\i:0.4) -- cycle;
  \draw [->, red, ultra thick] (0,0,0) -- (1,0,0);
  \draw [->, red, ultra thick] (0,0,0) -- (0,1,0);
  \draw [->, red, ultra thick] (0,0,0) -- (0,0,1);
\end{scope}

\draw [->, orange, ultra thick] (0,0,0) -- (0,1,0) node[black, anchor=south east] at (0, 1, 0) {$\vec{z_0}$};
\draw [canvas is zx plane at y=0.75, ->, blue] (0,-0.15) arc (-90:180:0.15);
\node at (0.3,0.9) {$\dot{\Psi}\vec{z_0}$};

\end{tikzpicture}
\end{document}