Ce document regroupe les codes TIKZ des figures utilisées pour le cours "CINEMATIQUE DU POINT" situé à la page : http://femto-physique.fr/mecanique/meca_C1.php
\begin
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% !TEX encoding = UTF-8 Unicode
% J.Roussel
% MAJ : 2014-06-03
% Ce document regroupe les codes TIKZ des figures utilisées pour le cours "CINEMATIQUE DU POINT" situé à la page http://femto-physique.fr/mecanique/meca_C1.php
%-------------------------------------------
\documentclass[11pt]{article}
\input{styles_meca}
\title{Figures TikZ du cours "CINEMATIQUE DU POINT"}
\begin{document}
% =================================================
% sujet : abscisse curviligne
% =================================================
\begin{tikzpicture} [scale=0.8]
\coordinate (A) at (0, -1);
\coordinate (M0) at (1,1);
\coordinate (M) at (3,1.5);
\coordinate (B) at (5,0);
\foreach \x in {(M0),(M)}
\draw[shift={\x}] node{$\bullet$};
\draw [trajet,->] (A) .. controls +(0.5,0.4) and +(-0.5,-1) .. (M0) .. controls +(0.5,1) and +(-0.4,0.8) .. (M).. controls +(0.4,-0.8) and +(-2,0) .. (B)node[right]{\small trajectoire};
\draw (M0)node[below right]{M$_0$};
\draw (M)node[above right]{M};
\draw[thick] (M0) .. controls +(0.5,1) and +(-0.4,0.8) .. (M);
\draw (2,2.5) node{$s(t)=\wideparen{\mathrm{M_0M}}$};
\end{tikzpicture}
% =================================================
% sujet : mouvement circulaire
% =================================================
\begin{tikzpicture} [scale=3,figure/.style={thick,color=#1,fill=purple, opacity=0.3},]
\colorlet{darkblue}{blue!50!black};
\coordinate (O) at (0, 0);
\coordinate (M) at (55:0.6);
\draw [axis] (-0.5,0)--(1,0);
\draw [axis] (0,-0.5) --(0,1);
\draw (0.2,0) node[below] {$\overrightarrow{{u}_{x}}$} ++(-0.2,0.2) node[below left] {$\overrightarrow{{u}_{y}}$};
\draw[figure=darkblue] (0,0) circle (0.6) ;
\draw (55:0.4) node[right]{$R$};
\draw (M) node[above right] {M($x(t)$,$y(t)$)};
\draw[thin,gray] (O)-- (M) node {$\bullet$};
\draw[vecteur] (O)-- ++(0.2,0);
\draw[vecteur] (O)-- ++(0,0.2);
\draw (O) node {$\bullet$} ++(1,0) node[below left] {$x$} ++(-1,1) node[below left] {$y$};
\draw (0.15,0) arc (0:55:0.15) ;
\draw (27:0.25) node {$\omega t$};
\end{tikzpicture}
% =================================================
% sujet : mouvement circulaire
% =================================================
\begin{tikzpicture} [scale=3,figure/.style={thick,color=#1,fill=purple, opacity=0.3},]
\colorlet{darkblue}{blue!50!black};
\coordinate (O) at (0, 0);
\coordinate (M) at (55:0.6);
\draw [axis] (-0.5,0)--(1,0);
\draw [axis] (0,-0.5) --(0,1);
\draw (0.2,0) node[below] {$\overrightarrow{{u}_{x}}$} ++(-0.2,0.2) node[below left] {$\overrightarrow{{u}_{y}}$};
\draw[figure=darkblue] (0,0) circle (0.6) ;
\draw (0.6,0) arc (0:55:0.6) ;
\draw (55:0.4) node[right]{$R$};
\draw (M) node[above right] {M($t$)};
\draw (0.6,0) node[above right] {M$_{0}$};
\draw[thin,gray] (O)-- (M) node {$\bullet$};
\draw[vecteur] (O)-- ++(0.2,0);
\draw[vecteur] (O)-- ++(0,0.2);
\draw (O) node {$\bullet$} ++(1,0) node[below left] {$x$} ++(-1,1) node[below left] {$y$};
\draw (0.15,0) arc (0:55:0.15) ;
\draw (27:0.25) node {$\omega t$};
\draw[->] ({sqrt(2)/2},{sqrt(2)/2}) arc (45:60:1)node[above]{+} ;
\end{tikzpicture}
% =================================================
% sujet : abscisse curviligne
% =================================================
\begin{tikzpicture} [scale=0.8]
\coordinate (A) at (0, -1);
\coordinate (M0) at (1,1);
\coordinate (M) at (3,1.5);
\coordinate (B) at (5,0);
\foreach \x in {(M0),(M)}
\draw[shift={\x}] node{$\bullet$};
\draw [trajet,->] (A) .. controls +(0.5,0.4) and +(-0.5,-1) .. (M0) .. controls +(0.5,1) and +(-0.4,0.8) .. (M).. controls +(0.4,-0.8) and +(-2,0) .. (B)node[right]{\small trajectoire};
\draw (M0)node[below right]{M$_0$};
\draw (M)node[above right]{M};
\draw[thick] (M0) .. controls +(0.5,1) and +(-0.4,0.8) .. (M);
\draw (2,2.5) node{$s(t)=\wideparen{\mathrm{M_0M}}$};
\end{tikzpicture}
% =================================================
% sujet : vecteur vitesse
% =================================================
\begin{tikzpicture} [scale=0.8]
\coordinate (A) at (0, -1);
\coordinate (M) at (1,1);
\coordinate (M') at (3,1.5);
\coordinate (B) at (5,0);
\foreach \x in {(M),(M')}
\draw[shift={\x}] node{$\bullet$};
\draw [trajet,->] (A) .. controls +(0.5,0.4) and +(-0.5,-1) .. (M) .. controls +(0.5,1) and +(-0.4,0.8) .. (M').. controls +(0.4,-0.8) and +
(-2,0) .. (B)node[right]{\small trajectoire};
\draw[vecteur] (M)node[below right]{M}--++(1,2) node[right]{$\overrightarrow{v}_{\rm M}\equiv \displaystyle{\lim_{\Delta t\rightarrow 0}}\overrightarrow{v}_{\rm MM'}$};
\draw[vecteur] (M)--(M')node[above right]{M'}--++(1,0.25) node[right]{$\overrightarrow{v}_{\rm MM'}$};
\end{tikzpicture}
% =================================================
% sujet : système cartésien
% =================================================
\begin{tikzpicture} [scale=0.8]
\coordinate (O) at (0, 0);
\coordinate (M) at (55:3);
\draw [axis] (-1,0)--(4,0);
\draw [axis] (0,-1) --(0,4);
\draw (1,0) node[below] {$\overrightarrow{{u}_{x}}$} ++(-1,1) node[below left] {$\overrightarrow{{u}_{y}}$};
\draw (M) node[above right] {M($t$)};
\draw[thin,->] (O)node {$\bullet$} -- (M) node {$\bullet$}node[midway,above,rotate=55]{$\overrightarrow{r}(t)$};
\draw[vecteur] (O)-- ++(1,0);
\draw[vecteur] (O)-- ++(0,1);
\draw[dashed]({3*cos(55)},0)node[below] {$x(t)$} --(M);
\draw[dashed](0,{3*sin(55)})node[left] {$y(t)$} --(M);
\end{tikzpicture}
% =================================================
% sujet : système polaire
% =================================================
\begin{tikzpicture} [scale=0.8]
\coordinate (O) at (0, 0);
\coordinate (M) at (55:3);
\draw [axis] (-1,0)--(4,0);
\draw [axis] (0,-1) --(0,4);
\draw (1,0) node[below] {$\overrightarrow{{u}_{x}}$} ++(-1,1) node[below left] {$\overrightarrow{{u}_{y}}$};
\draw[vecteur] (M)--++({-sin(55)},{cos(55)}) node[above right]{$\overrightarrow{u_{\theta}}$};
\draw[vecteur] (M)--++({cos(55)},{sin(55)}) node[above right]{$\overrightarrow{u_{r}}$};
\draw (55:1.5) node[above,rotate=55]{$r(t)$};
\draw (M) node[right] {M($r(t),\theta(t)$)};
\draw[thin,gray] (O)-- (M) node {$\bullet$};
\draw[vecteur] (O)--++(1,0);
\draw[vecteur] (O)-- ++(0,1);
\draw (O) node {$\bullet$} ++(4,0) node[below left] {$x$} ++(-4,4) node[below left] {$y$};
\draw[->] (1.2,0) arc (0:55:1.2) ;
\draw (27:1.2) node[above right] {$\theta(t)$};
\end{tikzpicture}
% =================================================
% sujet : repère de Frenet
% =================================================
\begin{tikzpicture} [scale=0.9,>=latex, inner sep=0pt, outer sep=2pt, axis/.style={thin,gray}, vecteur/.style=
{->,thick,color=black,smooth}, courbe/.style={thick,color=#1,smooth}]
\colorlet{darkblue}{blue!50!black};
\coordinate (O) at (0, 0);
\coordinate (N) at (0,-2);
\draw[courbe=darkblue, variable=\x, samples at={-1.6,-1.5,...,0.1}] plot ( { cos(\x r)}, { 2.0*sin(\x r)})
plot ( { -cos(\x r)}, { -2.0*sin(\x r)}) plot ( { cos(\x r)}, { -2.0*sin(\x r)}) plot ( { -cos(\x r)}, { 2.0*sin(\x r)});
\foreach \t in{0.7}{
\coordinate (M) at ({cos(\t r)},{2*sin(\t r)});
\coordinate (C) at ({-3*(cos(\t r))^3},{1.5*sin(\t r)^3});
\draw[dashed] (C) node{\tiny{$\bullet$}} node[below]{ $C$} circle ({0.5*(1+3*(cos(\t r))^2)^1.5}) -- (M) node{\tiny{$\bullet$}}
node[right]{M($t$)};
\draw[vecteur] (M)--++({-sin(\t r)},{2*cos(\t r)}) node [below right]{$\overrightarrow{t}$};
\draw[vecteur] (M)--++({-2*cos(\t r)},{-sin(\t r)}) node [below right]{$\overrightarrow{n}$};
\draw[thin,gray] (C)--++({-0.5*(1+3*(cos(\t r))^2)^1.5},0) node[midway,above]{$R(t)$};
}
\draw[vecteur] (N) node[below right]{Trajectoire} --++(0.1,0);
\end{tikzpicture}
% =================================================
% sujet : accélération
% =================================================
\begin{tikzpicture} [scale=1]
\coordinate (A) at (1,0);
\coordinate (M) at (1,1);
\coordinate (M') at (1.75,2);
\coordinate (B) at (6,0);
\draw[thin,gray,dashed] (M)--++(2,4);
\draw[thin,gray,dashed] (M')--++(3,3);
\draw [trajet,->] (A) .. controls +(-0.02,0.1) and +(-0.5,-1) .. (M) .. controls +(0.25,0.5) and +(-0.2,-0.2) .. (M').. controls +(2,2) and +
(-2,0) .. (B)node[right]{\small trajectoire};
\draw[vecteur,gray] (M)node[black,below right]{M}--++(1,2) node[left=4pt,black]{$\overrightarrow{v}_{\!\rm M}$};
\draw[vecteur,gray] (M')node[black,below right]{M'}--++(2,2) node[black,right]{$\overrightarrow{v}_{\!\rm M'}$};
\draw[vecteur] (M)--++(2,0) node[below]{$\overrightarrow{a}_{\!\rm M} =\lim\limits_{\Delta t\to 0} \dfrac{\Delta \overrightarrow{v}}{\Delta t}$};
\foreach \x in {(M),(M')}
\draw[shift={\x}] node{$\bullet$};
\end{tikzpicture}
\begin{tikzpicture}
\coordinate (M) at (1,1);
\coordinate (M') at (1.75,2);
\draw[thin,gray,dashed] (M)--++(2,4);
\draw[thin,gray,dashed] (M)--++(4,4);
\draw[vecteur,gray] (M)node[black,below right]{M}--++(1,2) node[left=4pt,black]{$\overrightarrow{v}_{\!\rm M}$};
\draw[vecteur,gray](M)--++(2,2)node[black,right]{$\overrightarrow{v}_{\!\rm M'}$};
\draw[vecteur,red](M)++(1,2)--(3,3) node[pos=0.5,above]{$\Delta \overrightarrow{v}$};
\draw[shift={(M)}] node{$\bullet$};
\end{tikzpicture}
% =================================================
% sujet : mouvement rectiligne
% =================================================
\begin{tikzpicture} [scale=0.8,]
\coordinate (O) at (0, 0);
\coordinate (M) at (5,1);
\draw [trajet] (-5,-1)--(10,2);
\draw (O) node[below right]{O}++(-0.02,0.1)--++(0.04,-0.2);
\draw (M) node {$\bullet$} node[below right]{M($t$)};
\draw[vecteur] (M)-- ++(1,0.2) node[above left]{$\overrightarrow{t}$};
\draw (2.5,0.5) node[below] {$s(t)$};
\draw[gray,thick](O)--(M);
\end{tikzpicture}
% =================================================
% sujet : mvt circulaire
% =================================================
\begin{tikzpicture} [scale=4,>=latex, inner sep=0pt, outer sep=2pt, axis/.style={thin,gray},
vecteur/.style={->,thick,color=black,smooth}, figure/.style={thick,color=#1,fill=purple, opacity=0.3},]
\colorlet{darkblue}{blue!50!black};
\coordinate (O) at (0, 0);
\coordinate (M) at (55:0.6);
\draw [axis] (-0.5,0)--(1,0);
\draw [axis] (0,-0.5) --(0,1);
\draw (0.2,0) node[below] {$\overrightarrow{{u}_{x}}$} ++(-0.2,0.2) node[below left] {$\overrightarrow{{u}_{y}}$};
\draw[figure=darkblue] (0,0) circle (0.6) ;
% \draw (0.6,0) arc (0:55:0.6) ;
\draw[vecteur] (M)--++(-0.273,0.191) node[above right]{$\overrightarrow{v}_{\!\rm M}$};
\draw (M) node[above right] {M$(t)$};
% \draw (0.6,0) node[above right] {$\mathrm{M_{0}}$};
\draw[thin,gray] (O)-- (M) node {$\bullet$}node[black,midway,above=4pt]{$R$};
\draw[vecteur] (O)-- ++(0.2,0);
\draw[vecteur] (O)-- ++(0,0.2);
\draw (O) node {$\bullet$} ++(1,0) node[below left] {$x$} ++(-1,1) node[below left] {$y$};
\draw[->] (0.2,0) arc (0:55:0.2) ;
\draw (27:0.3) node {$\theta(t)$};
\end{tikzpicture}
\end{document}