Math & Science ⇒ draw a graph

[magi6162]

I am a newbie to latex and also to this forum.
I have to draw in vector format as in the attached figure. I kindly ask for suggestions.
Thanks

[Stefan Kottwitz]

Welcome to the forum!

What is the math formula for that graph you want to draw?

Stefan

[magi6162]

I don't know it, so I was wondering if anyone on the forum knows it. (parametric also should work well with asymptote)
Thanks for the welcome and for the help.

[Stefan Kottwitz]

It looks like a copy from a book, so perhaps there is some math context for parametrization?

Stefan

[magi6162]

unfortunately no, it's just an example

[Stefan Kottwitz]

Ok, then here is a similar example:

Code: Select all

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\begin{document}
\begin{tikzpicture}
  \begin{polaraxis}[
      domain  = 0:1440,
      samples = 1000,
    ]
    \addplot[thick, blue] {sin(1.1*x)^2};
    \legend{$\sin(1.1x)^2$}
    \end{polaraxis}
\end{tikzpicture}
\end{document}

plot.png (34.38 KiB) Viewed 6832 times

Put in what you think the formula may be.

Seems the figure is from Landau and Lifshitz, Mechanics, Vol. 1, figure 9 in 14. Motion in a central field. That may explain how to (re)produce it.

It's also seen as figure 6.1 (Open path of a particle) from the paper KAM Stability of The Kepler Problem with a General Relativistic Correction Term by Majed Sofiani.

Stefan

[magi6162]

Thanks, invaluable help

[Stefan Kottwitz]

Here's a drawing repeating ellipses. This seems to come close, elliptic movements repeated.

Code: Select all

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\begin{document}
\begin{tikzpicture}
  \begin{polaraxis}[
      domain  = 0:360,
      samples = 100,
    ]
    \foreach \w in {0,30,...,360} {
      \addplot[thick, blue] {(1*(1-0.8^2)/(1+0.8*cos(x+\w))};}
    \end{polaraxis}
\end{tikzpicture}
\end{document}

plot-ellipses.png (39.91 KiB) Viewed 6829 times

You can compare the formula to the equation 3.2 in the appendix of the article I linked above.

With an arrow decoration macro from the pgfplots author Christian Feuersänger:

Code: Select all

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\usepgfplotslibrary{colormaps}
\usetikzlibrary{decorations.markings}
\tikzset{
  set arrow inside/.code={\pgfqkeys{/tikz/arrow inside}{#1}},
  set arrow inside={end/.initial=>, opt/.initial=},
  /pgf/decoration/Mark/.style={
    mark/.expanded=at position #1 with
    {
      \noexpand\arrow[\pgfkeysvalueof{/tikz/arrow inside/opt}]{\pgfkeysvalueof{/tikz/arrow inside/end}}
    }
  },
  arrow inside/.style 2 args={
    set arrow inside={#1},
    postaction={
      decorate,decoration={
        markings,Mark/.list={#2}
      }
    }
  },
}
\begin{document}
\begin{tikzpicture}
  \begin{polaraxis}[
      domain  = 0:360,
      samples = 100,
    ]
    \foreach \w in {0,30,...,360} {
      \addplot[thick, blue] {(1*(1-0.8^2)/(1+0.8*cos(x+\w))} [arrow inside={end=stealth,opt={black, scale=1.05}}{0.5}];}
    \end{polaraxis}
\end{tikzpicture}
\end{document}

plot-with-arrows.png (40.47 KiB) Viewed 6829 times

Stefan

[Stefan Kottwitz]

And with the option hide axis:

plot-hidden-axis.png (21.34 KiB) Viewed 6825 times

Code: Select all

\begin{polaraxis}[
      domain  = 0:360,
      samples = 100,
      hide axis,
    ]
    ...

Stefan

[magi6162]

I have no words for the help you have given me. Thank you so much