Ich versuche, ein Flugbahndiagramm nachzubilden, um Stabilität zu demonstrieren. Das Bild, das mir vorschwebt, ähnelt in etwa der folgenden Abbildung:
Das Problem ist, dass ich nicht wirklich weiß, wie ich die Linientrajektorie erzeugen soll, da ich keine numerischen Daten habe, auf die ich mich stützen könnte. Die Form der Trajektorie ist irrelevant, solange sie asymptotisches Verhalten zeigt. Sie sollte vorzugsweise so aussehen wie in der Abbildung. Ich werde meinen aktuellen Fortschritt im folgenden Code anhängen:
\documentclass[tikz]{standalone}
\usepackage{geometry}
\usepackage{pgfplots}
\usepackage{bm}
\usetikzlibrary{3d,calc}
\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture}%[show grid=all]
% background
\path[name path=C] (-1.5,1.75) -- (1.5,3.25);
\path[name path=D] (-1.5,-1.5) -- (1.5,0.5);
\tikzfillbetween[of=C and D]{top color=gray!10!white, bottom color=white, opacity=0.02};
% axis
\draw[gray!50!white,->,very thick,>=latex] (0,-0.5) -- (0,2.5);
\draw[gray!50!white,->,very thick,>=latex] (1.5,1.75) -- (-1.5,0.25);
\draw[gray!50!white,->,very thick,>=latex] (0,1) -- (7,1);
\filldraw[black] (0,1) circle (1.2pt);
\filldraw[black] (6,1) circle (1.2pt);
\draw[blue!50!white,dashed,very thick] (0,0) arc (-90:90:0.6cm and 1cm);
\draw[blue!50!white,thick] (0,0) arc (-90:90:-0.6cm and 1cm);
\draw[blue!50!white,thick] (6,0.5) arc (-90:90:-0.4cm and 0.5cm);
\draw[blue!50!white,thick] (6,0.5) arc (-90:90:0.4cm and 0.5cm);
\draw[blue!50!white,thick,name path = A] (0,2) to[in=180,out=-12] (6,1.5);
\draw[blue!50!white,thick,name path = B] (0,0) to[in=180,out=12] (6,0.5);
\tikzfillbetween[of=A and B]{blue!50!white, opacity=0.2};
\shade[left color=blue!50!white,right color=blue!50!white,opacity=0.2] (0,0) arc (-90:90:-0.6cm and 1cm);
\shade[left color=blue!50!white,right color=blue!50!white,opacity=0.2] (6,0.5) arc (-90:90:0.4cm and 0.5cm);
% axis labels
\node at (0,2.9) {$\varphi_{1}(t)$};
\node at (-2,0.21) {$\varphi_{2}(t)$};
\node at (7.15,1) {$t$};
\draw[thick,->,>=latex] (0,1) -- (0,2) node [midway,scale=0.9,right]{$\delta$};
\draw[thick,->,>=latex] (6,1) -- (6,1.5) node [midway,scale=0.9,right]{$\varepsilon$};
\draw[dashed,blue] (-0.3,1.35) -- (-2,2.5) node [pos=1.2,text=black,scale=0.9]{$\bm{\varphi}(0)$};
% trajectory
\filldraw[blue!90!white] (-0.3,1.35) circle (1.2pt);
% border adjustment (standalone crop problems)
\node at (0,-2.3) {$$};
\node at (8,0) {$$};
\end{tikzpicture}
\end{document}
Antwort1
Ich konnte die Antwort von
Schleifen planen: Flugbahnen und Richtungen
um die folgende Flugbahn zu zeichnen:
Hier ist der Code:
\documentclass[tikz]{standalone}
\usepackage{geometry}
\usepackage{pgfplots}
\usepackage{bm}
\usetikzlibrary{3d,calc}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{arrows.meta,hobby}
\begin{document}
\begin{tikzpicture}[use Hobby shortcut]%[show grid=all]
\tikzset{axisArrow/.style={gray!50!white,very thick,>=stealth,arrows={->[fill=black]}}}
% background
\path[name path=C] (-1.5,1.75) -- (1.5,3.25);
\path[name path=D] (-1.5,-1.5) -- (1.5,0.5);
\tikzfillbetween[of=C and D]{top color=gray!10!white, bottom color=white, opacity=0.02};
% axis
\draw[axisArrow] (0,-0.5) -- (0,2.5);
\draw[axisArrow] (1.5,1.75) -- (-1.5,0.25);
\draw[axisArrow] (0,1) -- (7,1);
\filldraw[black] (0,1) circle (1.2pt);
\filldraw[black] (6,1) circle (1.2pt);
\draw[blue!50!white,dashed, thick] (0,0) arc (-90:90:0.6cm and 1cm);
\draw[blue!50!white,thick] (0,0) arc (-90:90:-0.6cm and 1cm);
\draw[blue!50!white,thick] (6,0.5) arc (-90:90:-0.4cm and 0.5cm);
\draw[blue!50!white,thick] (6,0.5) arc (-90:90:0.4cm and 0.5cm);
\draw[blue!50!white,thick,name path = A] (0,2) to[in=180,out=-12] (6,1.5);
\draw[blue!50!white,thick,name path = B] (0,0) to[in=180,out=12] (6,0.5);
\tikzfillbetween[of=A and B]{blue!50!white, opacity=0.2};
\shade[left color=blue!50!white,right color=blue!50!white,opacity=0.2] (0,0) arc (-90:90:-0.6cm and 1cm);
\shade[left color=blue!50!white,right color=blue!50!white,opacity=0.2] (6,0.5) arc (-90:90:0.4cm and 0.5cm);
% axis labels
\node at (0,2.9) {$\varphi_{1}(t)$};
\node at (-2,0.21) {$\varphi_{2}(t)$};
\node at (7.15,1) {$t$};
\node[scale=0.7] at (5,1.65) {$t\rightarrow \infty$};
\draw[thick,->,>=stealth] (0,1) -- (0,2) node [midway,scale=0.9,right]{$\delta$};
\draw[thick,->,>=stealth] (6,1) -- (6,1.5) node [midway,scale=0.9,right]{$\varepsilon$};
\draw[dashed,blue] (-0.3,1.35) -- (-2,2.5) node [pos=1.2,text=black,scale=0.9]{$\bm{\varphi}(0)$};
% trajectory
\filldraw[blue!90!white] (-0.3,1.35) circle (1.2pt);
\draw[-stealth,blue!90!white,thick] (-0.3,1.35) .. (1,0.5) .. (1.75,1.4) .. (1.5,1.2) .. (2,1.2) .. (2.5,1.1) .. (3,0.9) .. (3,1) .. (4,1) .. (4.3,1) .. (4.8,1) -- (5.55,1);
% border adjustment (standalone crop problems)
\node at (0,-2.3) {$$};
\node at (8,0) {$$};
\end{tikzpicture}
\end{document}