\documentclass[a4]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage[usenames,dvipsnames]{xcolor}
%\usepackage{tikz}

\usepackage{pgfplots}
\usepackage{tikz,animate}
\usepackage{pgfplots}
\usetikzlibrary{shapes.arrows}
\usetikzlibrary{arrows.meta}

\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}
\pagestyle{empty}


\includegraphics[width=0.6\linewidth, height=0.6\linewidth]{Fig10_domain.pdf}

\vspace{-8.53cm}\hspace{-1.22cm}
\begin{tikzpicture}[>={Stealth[scale=1]}]

\draw[->,  ultra thick] (0,0) -- (8.0, 0);
\draw (8.0,-0.8) node [text=black]{{\Large $\theta_1$}};

\draw[->,  ultra thick] (0,0) -- (0, 8.0);
\draw (-0.9,8) node [text=black]{{\Large  $\theta_2$}};

\draw[-, ultra thick](3.5,0) -- (3.5,0.2);
%\draw[-, thick](6.95,0) -- (6.95,6.75);
\draw[-,  ultra thick](7.0,0) -- (7.0,7.0);



\draw[-, ultra thick](0,3.5) -- (0.2,3.5);
\draw[-, ultra thick](0,7.0) -- (7.0,7.0);

\draw (-0.5,3.5) node [text=black]{{\large  $\pi/2$}};
\draw (-0.5,6.75) node [text=black]{{\large  $\pi$}};

\draw (3.5, -0.5) node [text=black]{{\large  $\pi/2$}};
\draw (7.0,-0.5) node [text=black]{{\large  $\pi$}};

\draw (3.5, 3.5) node [text=black]{ 3.9};
\draw (4.4, 4.4) node [text=black]{3.0};
\draw (5.05, 5.05) node [text=black]{2.5};
\draw (5.95, 5.95) node [text=black]{2.1};
\end{tikzpicture}



\end{document}



\begin{tikzpicture}
% z- axis
% upper circle

\draw[->,thick, red] (0,0) -- (-0.866025,0.5);
\draw (-0.75,0.2) node [text=red]{ $R_1$};
\draw[-,thin] (-2.5,0) -- (1.8,0);
\draw[thick] (0,-3) circle (1.5);
\draw[thick, blue] (0,-1.29167) circle (0.817559);
\draw[thin, blue] (-2,-1.29167) -- (1.8,-1.29167);
\draw[-,thin] (-2.5,-3) -- (1.8,-3);
\draw[->,thin] (-2.3,-1.4) -- (-2.3,0);
\draw[->, thin] (-2.3,-1.9) -- (-2.3,-3);
\draw (-2.3,-1.65) node [text]{$a$};
\draw[->, thin,blue] (-2.0,-0.4) -- (-2.0, 0.0);
\draw[->, thin,blue] (-2.0,-0.8) -- (-2.0, -1.29167);
\draw (-1.9, -0.6) node [text=blue]{$a_1$};
\draw[->, thin, blue] (-2.0, - 2.0) -- (-2.0,-1.29167) ;
\draw[->, thin, blue] (-2.0, -2.4) -- (-2.0, -3.0);
\draw (-1.9,-2.2) node [text=blue]{$a_2$};
\draw (2.0, -1.0) node [text=blue]{$M$};
\draw (0.2, 1.2) node [text]{$A$};
\draw (0.2, 0.2) node [text]{$B$};
\draw (0.2, -0.3) node [text]{$C$};
\draw (0.2, -0.8) node [text]{\small $D$};
\draw (0.2, -1.15) node [text]{\small $E$};
\draw (0.2, -1.4) node [text]{\tiny $F$};
\end{tikzpicture}


\begin{tikzpicture}
\draw[->, ultra thick] (-1,0) -- (2.5,0);
\draw (2.5,-0.5) node {\Large $x$};
\draw[->, ultra thick] (0,-2.5) -- (0,1);
\draw (-0.5,1) node {\Large $z$};
\draw[-,ultra thick, blue] (0,0) -- (1,-2);
\draw[thick, blue,fill=blue] (1,-2) circle  (0.2);
\draw (1.6,-2.2) node [text=blue]{\Large $m$};
\draw[->,,thick] (0,-1.5) arc[radius=1.2, start angle=270, end angle=300];
%\draw[-,,thick] (-2.,-1.25) arc[radius=2.25, start angle=210, end angle=330];
\draw[thick] (0,0) circle (2.25);
\draw [->, ultra thick, red] (1.5,-0.5) -- (1.5,-1.5);
\draw (0.8,-1.0) node [text=blue]{\Large $l$};
\draw (1.8,-1.0) node [text=red]{\Large $g$};
%pic [draw, ->,''$\varphi$'', angle eccentricity=5.5] {angle =(0,-2) -- (0,0) -- (1,-2)};
\end{tikzpicture}






