Kraftmoment

Question

Ich habe viel gegoogelt, aber nichts Relevantes gefunden. Wie erstelle ich in Tikz die folgende Abbildung?

https://fr.wikipedia.org/wiki/Moment_d%27une_force#/media/Fichier:Momento_de_uma_for%C3%A7a..png

Hier ist, was ich bisher getan habe.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}

    % Define angle and force magnitude
    \def\angle{70} % Angle in degrees
    \def\Fnorm{3} % Magnitude of the force vector

    % Define coordinates
    \coordinate (O) at (0,0); % Origin
    \coordinate (P) at (1,1); % tail of force 
    \coordinate (F) at ({1 + \Fnorm * cos(\angle)}, {1 + \Fnorm * sin(\angle)}); % Force head
% Calculate coordinates for point Q
\coordinate (Q) at ({1 + 1.2*cos(\angle)}, {1 + 1.2*sin(\angle)});

    % Draw the force vector
    \draw[-latex, thick, blue] (P) -- (F) node[midway, right] {$\vec{F}$};
            
%      Draw position vectors
    \draw[-latex, thick, red] (O) -- (P) node[midway, right] {$\vec{r}$};
        \draw[-latex, thick, orange] (O) -- (Q) node[midway, left] {$\vec{r'}$};
    
        \fill (Q) circle[radius=1pt] node[  left] {$Q$};
        
                \fill (P) circle[radius=1pt] node[below right] {$P$};

        \fill (O) circle[radius=1pt] node[ below] {$O$}; % origin

\end{tikzpicture}

\end{document}

Wie kann ich einfach die Projektionen entlang der Richtung des Vektors OP und normal dazu, den Hebelarm und den geschweiften Vektor, der den Momentenvektor darstellt, erhalten?

Vielen Dank für jede Hilfe.

Answer 1

Aktualisieren

Um eine PFdreimal längere Länge zu erhalten OP, verwende ich die letOperation.

\path let  \p1=($(P)-(O)$),
            \n1 = {veclen(\x1,\y1)},
            in 
(O)--(P)--([turn]\angle:\n1*\Fnorm])coordinate (F);

Ich habe die Art und Weise geändert, wie Sie die Koordinaten definieren, um die Berechnungen zu vereinfachen. Und ich habe viele Änderungen vorgenommen, sodass ich nicht die Zeit habe, sie alle zu erklären. Ich lasse Sie einen Blick auf den Code werfen, und wenn Sie etwas nicht verstehen, sagen Sie es einfach und ich werde es Ihnen erklären.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,angles}

\begin{document}

\begin{tikzpicture}[every node/.style={font=\footnotesize}]

    % Define angle and force magnitude
    \def\angle{60} % Angle in degrees
    \def\Fnorm{3} % Magnitude of the force vector

    % Define coordinates
    \coordinate[label=left:O] (O) at (0,0); % Origin
    \coordinate (P) at (2,1); % tail of force 

    \path let  \p1=($(P)-(O)$),
                \n1 = {veclen(\x1,\y1)},
                in 
    (O)--(P)--([turn]\angle:\n1*\Fnorm])coordinate (F);
    \coordinate[label=left:Q] (Q) at ($(P)!.4!(F)$);
    \fill (Q) circle[radius=1pt];

    % Draw the force vector
    \draw[-latex, thick, blue] (P) -- (F) node[midway, right] {$\vec{F}$};
            
%      Draw position vectors
    \draw[-latex, thick, red] (O) -- (P) node[midway, above,yshift=-3pt] {$\vec{r}$};
        \draw[-latex, thick, orange] (O) -- (Q) node[midway, left] {$\vec{r'}$};
           
        \fill (P) circle[radius=1pt] node[below right] {$P$};

        \fill (O) circle[radius=1pt];% node[ below] {$O$}; % origin
        
        \coordinate (H) at ($(O)!(F)!(P)$);
        \draw(F)--(H)node[midway,right]{$F\sin\theta$};
        \draw[dashed] (P)--($(P)!1.2!(H)$);
        \coordinate(H') at ($(F)!(O)!(P)$);
        \draw(O)--(H')node[midway,sloped,below]{$r\sin\theta$};
        \draw[dashed] (P)--($(P)!1.5!(H')$);
        \pic[draw,pic text=$\theta$,angle radius=4mm,angle eccentricity=1.35]{angle=O--P--H'};
        \pic[draw,pic text=$\theta$,angle radius=4mm,angle eccentricity=1.35]{angle=H--P--F};
        
        \node[inner sep=0pt] (Mo) at (barycentric cs:O=1,P=-.5 ,F=1){$M_o$};
        \draw[->,very thick, blue] (Mo.south west)to[out=-90,in=-90,looseness=2](Mo.south east);
\end{tikzpicture}

\end{document}

Answer 2

Ich poste meinen aktualisierten Code als Antwort. Weit entfernt vom Wiki-Bild, aber trotzdem kann er für andere nützlich sein.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{amsmath} % for trigonometric functions

\begin{document}

\begin{tikzpicture}
    % Draw axes
    \draw[->] (-0.5,0) -- (3,0) node[right] {$x$};
    \draw[->] (0,-0.5) -- (0,3) node[above] {$y$};

    % Define point P
    \coordinate (P) at (1,1);
    
    % Define point O
    \coordinate (O) at (0,0);

    % Calculate coordinates of point Q
    \pgfmathsetmacro{\phhi}{60} % angle in degrees
    \pgfmathsetmacro{\magnitude}{3} % magnitude of vector PQ
    \pgfmathsetmacro{\qx}{\magnitude * cos(\phhi)} % x-coordinate of Q
    \pgfmathsetmacro{\qy}{\magnitude * sin(\phhi)} % y-coordinate of Q

    % Define point Q
    \coordinate (Q) at ({1 + \qx}, {1 + \qy});
    
    % Calculate coordinates for parallel and perpendicular components of F
    \pgfmathsetmacro{\thheta}{45} % angle in degrees
    \pgfmathsetmacro{\parallelX}{\magnitude * cos(\phhi-\thheta)*cos(\thheta)} % x-coordinate of F_parallel
    \pgfmathsetmacro{\parallelY}{\magnitude * cos(\phhi-\thheta)*sin(\thheta)} % y-coordinate of F_parallel
    \coordinate (R) at ({1 + \parallelX}, {1 + \parallelY}); % Endpoint of F_parallel
    
    \pgfmathsetmacro{\perpendicularX}{\magnitude * sin(\phhi-\thheta)*sin(\thheta)} % x-coordinate of F_perpendicular
    \pgfmathsetmacro{\perpendicularY}{\magnitude * sin(\phhi-\thheta)*cos(\thheta)} % y-coordinate of F_perpendicular
    \coordinate (S) at ({1 - \perpendicularX}, {1 + \perpendicularY}); % Endpoint of F_perpendicular
    
    % Calculate coordinates of point T
    \pgfmathsetmacro{\Tx}{sqrt(2) * cos(90-\phhi) * sin(\phhi-\thheta)} % x-coordinate of T
    \pgfmathsetmacro{\Ty}{-sqrt(2) * sin(90-\phhi) * sin(\phhi-\thheta)} % y-coordinate of T
    % Define point T
    \coordinate (T) at (\Tx, \Ty);

    % Draw vector PQ
    \draw[-latex, thick] (P) -- (Q) node[midway, above] {$\vec{F}$};
    
    % Draw vector OP
    \draw[-latex, thick] (O) -- (P) node[midway, above] {$\vec{r}$};
    
    % Draw vector F_parallel
    \draw[-latex, thick] (P) -- (R) node[midway, below right] {$\vec{F_{\parallel}}$};
    
    % Draw vector F_perpendicular
    \draw[-latex, thick] (P) -- (S) node[midway, left] {$\vec{F_{\perp}}$};

    % Draw point P
    \fill (P) circle[radius=2pt] node[below right] {$P$};
    
    % Draw point O
    \fill (O) circle[radius=2pt] node[below left] {$O$};
    
    % Draw dashed lines for projections
    \draw[dashed] (S) -- (Q) -- (R);
    
    % Draw arc for angle theta
    \draw (0.5,0) arc[start angle=0,end angle=45,radius=0.5cm];
    \node at (0.7,0.3) {$\theta$}; % Label for angle theta
    
    % Draw the arc for angle phi
    \draw (1,1) +(0:0.5cm) arc[start angle=0, end angle=\phhi, radius=0.5cm];
    \node at (1.6,1.3) {$\phi$}; % Label for angle phi
    
    % Draw arc for angle phi - theta
    \draw (1,1) +(\thheta:1cm) arc[start angle=\thheta, end angle=\phhi, radius=1cm];
    \node at (1.65,1.9) {$\alpha$}; % Label for angle phi - theta
   
    % Draw dotted line from P to (2,1)
    \draw[dotted] (P) -- (2,1);
   
    % Draw dashed line from O to T
    \draw[dashed] (O) -- (T);
   
    % Draw dashed line from P to T
    \draw[dashed] (P) -- (T);

\end{tikzpicture}

\end{document}

Answer 3

Ausgehend von AndréCs Code mit tkz-elementsdefinieren wir die Punkte mit tkz-euclideoder tikzführen die Diagramme aus.

Der Code

% !TeX program = lualatex
\documentclass{standalone}
\usepackage{tkz-elements}
\usepackage{tkz-euclide}
\begin{document}
\begin{tkzelements}
    angle = math.pi/3
    Fnorm = 3
    --
    z.O  = point: new (0,0)
    z.P  = point: new (2,1)
    --
    -----------------------------
    -- translation and rotation
    V.v = vector: new (z.O,z.P)
    V.w = Fnorm*V.v
    -- in one step
    z.F  = z.P : rotation (angle,V.w.head : at (z.P))
    --
    --   or in two steps
    --z.Pp = V.w.head : at (z.P)
    -- rotation
    --z.F  = z.P : rotation (angle,z.Pp)
--------------------------------------
L.PF  = line : new (z.P,z.F)
z.Q   = L.PF : barycenter (6,4)
-- projection
z.Op  = L.PF: projection(z.O)
L.OP  = line : new (z.O,z.P)
z.Fp  = L.OP: projection(z.F)
\end{tkzelements}

\tkzSetUpLabel[font=\footnotesize]
\begin{tikzpicture}
    %\draw[help lines] (0,0)grid(8,8);
\tkzGetNodes
% points
\tkzDrawPoints(O,P,F,Q,O',F')
\tkzLabelPoints[below right](P)
\tkzLabelPoints[left](O,F,Q)
% line
\tkzDrawLine[dashed,add = 0 and 0.25](P,O')
\tkzDrawLine[dashed,add = 0 and 0.25](P,F')
% vecteurs
\tkzDrawSegments[-latex, thick, blue](P,F)
\tkzDrawSegments[-latex, thick, red](O,P)
\tkzDrawSegments[-latex, thick, orange](O,Q)
\tkzDrawSegments(O,O' F,F')
%
\tkzLabelSegment[blue,right](P,F){$\vec{F}$}
\tkzLabelSegment[red,above](O,P){$\vec{v}$}
\tkzLabelSegment[orange,above](O,Q){$\vec{r'}$}
\tkzLabelSegment[sloped,below](O,O'){$r\sin\theta$}
\tkzLabelSegment[right](F,F'){$F\sin\theta$}
% angle
\tkzMarkAngles[size = 0.4](O,P,O' F',P,F)
\tkzLabelAngle[pos=0.6](O,P,O'){$\theta$}
\tkzLabelAngle[pos=0.6](F',P,F){$\theta$}
% code AndréC
\node[inner sep=0pt] (Mo) at (barycentric cs:O=1,P=-.5 ,F=1){$M_o$};
\draw[->,very thick, blue] (Mo.south west)to[out=-90,in=-90,looseness=2](Mo.south east);
\end{tikzpicture}

\end{document}

BEARBEITEN: Mit tkz-elementshabe ich versucht, die Matrix-Klasse zu verwenden

    % !TeX program = lualatex
    \documentclass{article}
    \usepackage{amsmath}
    \usepackage{tkz-elements}
    \usepackage{tkz-euclide}
    \begin{document}
    \begin{tkzelements}
        z.P     = point : new (2,1)
        angle   = math.pi/3
        Fnorm   = 3
        -----------------------------
        z.O     = point : new (0,0)
        V.OP     = z.P.mtx : homogenization ()
        --V.OP : print () tex.print('\\\\')
        --
        M       = matrix : htm (angle , z.P.re , z.P.im)
        --M : print () tex.print('\\\\')
        S       = matrix : square (3,Fnorm,0,0,0,Fnorm,0,0,0,1)
        --S : print () tex.print('\\\\')
        V.F      = M * S * V.OP
        --V.F : print () tex.print('\\\\')
        z.F = get_htm_point(V.F)
        --tex.print(display(z.F))
        --------------------------------------
        L.PF  = line : new (z.P,z.F)
        z.Q   = L.PF : barycenter (6,4)
        -- projection
        z.Op  = L.PF: projection(z.O)
        L.OP  = line : new (z.O,z.P)
        z.Fp  = L.OP: projection(z.F)
    \end{tkzelements}


    \tkzSetUpLabel[font=\footnotesize]
    \begin{tikzpicture}[gridded]
        \tkzGetNodes
        % points
        \tkzDrawPoints(O,P,F,Q,O',F')
        \tkzLabelPoints[below right](P)
        \tkzLabelPoints[left](O,F,Q)
        % line
        \tkzDrawLine[dashed,add = 0 and 0.25](P,O')
        \tkzDrawLine[dashed,add = 0 and 0.25](P,F')
        % vecteurs
        \tkzDrawSegments[-latex, thick, blue](P,F)
        \tkzDrawSegments[-latex, thick, red](O,P)
        \tkzDrawSegments[-latex, thick, orange](O,Q)
        \tkzDrawSegments(O,O' F,F')
        %
        \tkzLabelSegment[blue,right](P,F){$\vec{F}$}
        \tkzLabelSegment[red,above](O,P){$\vec{v}$}
        \tkzLabelSegment[orange,above](O,Q){$\vec{r'}$}
        \tkzLabelSegment[sloped,below](O,O'){$r\sin\theta$}
        \tkzLabelSegment[right](F,F'){$F\sin\theta$}
        % angle
        \tkzMarkAngles[size = 0.4](O,P,O' F',P,F)
        \tkzLabelAngle[pos=0.6](O,P,O'){$\theta$}
        \tkzLabelAngle[pos=0.6](F',P,F){$\theta$}
        % code AndréC
        \node[inner sep=0pt] (Mo) at (barycentric cs:O=1,P=-.5 ,F=1){$M_o$};
        \draw[->,very thick, blue] (Mo.south west)to[out=-90,in=-90,looseness=2](Mo.south east);
    \end{tikzpicture}
    \end{document}