animation

用TikZ与animate包实现几个pdf动画效果

animate包可以调用Javascript来在pdf上实现一些动画效果，不过这个动画效果需要支持Javascript的pdf阅读器才能看到。这一期我们就来分别做几个物理动画：弹簧振子，单摆和圆锥摆的运动，代码需要编译两次，最好是pdflatex编译，然后用Adobe Reader就能看到动画效果了。
https://zhuanlan.zhihu.com/p/338402487
动画效果可以在我的知乎主页查看

弹簧振子

\documentclass{beamer}
\usepackage[autoplay]{animate}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing,patterns}
\begin{document}
\begin{frame}{}
\centering
\begin{animateinline}[loop]{20}%
  \multiframe{360  }{rx=0+5}{
\begin{tikzpicture}[scale=1.5]
\pgfmathsetmacro{\x}{4+1*sin(\rx)}	
\coordinate  (P) at (\x,0);	
\draw [decorate,decoration={coil,segment length= \x pt, pre length=2mm, post length=2mm
,amplitude=2mm}] (0,0)--(P);
\shade[ball color=black](P)circle (2mm);
\fill [pattern = north east lines] (0,0.-0.2) -- ++ (0,0.4) -- ++ (-0.1,0) -- ++(0,-0.4) --cycle
      (0,-0.2) -- ++(0,-0.1) -- ++ (5.5,0) -- ++ (0,0.1) -- cycle;
\draw (0,0.2) -- (0,-0.2) -- (5.5,-0.2);
\end{tikzpicture} 	    }
\end{animateinline}
\end{frame}
\end{document}

单摆

\documentclass{standalone}
\usepackage[autoplay]{animate}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}

\begin{animateinline}[loop]{20}%
  \multiframe{60  }{rt=-120+1}{
\begin{tikzpicture}[scale=1.5]
\filldraw [densely dashed,draw=black,fill=blue!20](0,0) -- (0,-1.5)
(0,0) -- (-120:1.5) (0,0) -- (-60:1.5) arc (-60:-120:1.5);
\draw (-2,-2) rectangle (2,1);
\pgfmathsetmacro{\x}{1.5*cos(\rt)}	
\pgfmathsetmacro{\y}{1.5*sin(\rt)}
\coordinate  (P) at (\x,\y);	
\draw[blue] (0,0)--(P);
\shade[ball color=black](P)circle (2pt);
\fill [pattern = north east lines] (-1,0) -- (1,0) -- (1,0.1) -- (-1,0.1) -- cycle;
\draw (-1,0) -- (1,0);
\end{tikzpicture} 	    }
\newframe
\multiframe{60  }{rt=-60+-1}{
\begin{tikzpicture}[scale=1.5]
\filldraw [densely dashed,draw=black,fill=blue!20](0,0) -- (0,-1.5)
(0,0) -- (-120:1.5) (0,0) -- (-60:1.5) arc (-60:-120:1.5);
\draw (-2,-2) rectangle (2,1);
\pgfmathsetmacro{\x}{1.5*cos(\rt)}	
\pgfmathsetmacro{\y}{1.5*sin(\rt)}
\coordinate  (P) at (\x,\y);	
\draw (0,0)--(P);
\shade[ball color=black](P)circle (2pt);
\fill [pattern = north east lines] (-1,0) -- (1,0) -- (1,0.1) -- (-1,0.1) -- cycle;
\draw (-1,0) -- (1,0);
\end{tikzpicture} 	    }

\end{animateinline}
\end{document}

圆锥摆

\documentclass{standalone}
\usepackage[autoplay]{animate}
\usepackage{tikz}
\usetikzlibrary{patterns,arrows.meta}
\begin{document}

\begin{animateinline}[loop]{20}%
  \multiframe{72  }{rt=0+-5}{
\begin{tikzpicture}[scale=1.5]
\draw (-2,-2) rectangle (2,1);
\pgfmathsetmacro{\x}{0.75*cos(\rt)}	
\pgfmathsetmacro{\y}{-1.3+0.3*sin(\rt)}	
\coordinate  (P) at (\x,\y);	
\draw [blue] (0,0)--(P);
\shade[ball color=black] (P) circle (2pt);
\fill [pattern = north east lines] (-1,0) -- (1,0) -- (1,0.1) -- (-1,0.1) -- cycle;
\draw (-1,0) -- (1,0);
\draw[red,densely dashed] (0,-1.3)ellipse (0.75 and 0.3);
\fill[opacity=0.1,red] (0,0) -- (0.75,-1.3)
arc (0:\rt:0.75 and 0.3) -- cycle;
\draw[-Stealth] (-0.5,-0.5) -- ++ (0,-0.3)node[right]{$g$};
\draw [densely dashed](0,0) -- (0,-1.3) -- node[above]{$r$}
(P) node[above right]{$m$};
\end{tikzpicture} 	    }
\end{animateinline}


\end{document}

心形线

\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphicx}
\usepackage[autoplay]{animate}
\begin{document}
\begin{animateinline}[loop]{12}%
  \multiframe{72}{ix = 0 + 5}{
   \begin{tikzpicture}
    \draw [line width = 0pt] (-3,-2) rectangle (2,2);
    \begin{scope}[xshift=-0.5cm]
      \draw[blue] (0,0) circle (0.5);
      \draw[green] (\ix:1) circle (0.5);
    \end{scope}
    \node at (0.5,1.7) {$r=1-\cos\theta$};
    \draw[domain=0:\ix,samples=500,red] plot ({(1-cos(\x))*cos(\x)},{(1-cos(\x))*sin(\x)});
  \end{tikzpicture} 	
  }
\end{animateinline}

\end{document}

旋轮线

\documentclass{standalone}
\usepackage{tikz,amsmath}
\usepackage{graphicx}
\usepackage[autoplay]{animate}
\usetikzlibrary{arrows.meta}
\tikzset{>=Stealth}
\begin{document}
\begin{animateinline}[loop]{10}%
  \multiframe{60}{rx = 0 + pi/30}{
  \begin{tikzpicture}
    \draw [->] (-1,0) -- (0,0) node[below left]{$O$} 
               -- (2*pi,0) node[below]{$2\pi$} 
               -- (7,0) node[below]{$x$};
    \draw [->] (0,-2) -- (0,2.4) node[left]{$y$};
    \node at (3,-1) {$\begin{cases}
      x = t - \sin t \\
      y = 1 - \cos t
    \end{cases}$};
    \draw [blue] (\rx,1) circle (1);
    \draw [domain=0:\rx,red] plot({\x-sin(\x r)},{1-cos(\x r)});
  \end{tikzpicture}
  }
\end{animateinline}
\end{document}

星形线

\documentclass{standalone}
\usepackage{tikz,amsmath}
\usepackage{graphicx}
\usepackage[autoplay]{animate}
\usetikzlibrary{arrows.meta}
\tikzset{>=Stealth}
\begin{document}
\begin{animateinline}[loop]{10}%
  \multiframe{60}{rx = 0 + 6}{
  \begin{tikzpicture}
    \draw [->] (-5,0) -- (0,0) node[below left]{$O$}
               -- (5,0)  node[below]{$x$};
    \draw [->] (0,-5) -- (0,5) node[left]{$y$};
    \draw (0,0) circle (4) ;
    \draw [blue] (\rx:3) circle (1);
    \node at (4,4) {$\begin{cases}
      x = a\cos ^3t\\
      y = a\sin ^3 t
    \end{cases}$};
    \draw [domain=0:\rx,red,samples=200] plot({4*(cos(\x))^3},{4*(sin(\x))^3});
  \end{tikzpicture}
  }
\end{animateinline}

\end{document}

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