diff --git a/is/ub7/is7.pdf b/is/ub7/is7.pdf index 2d8ad27..a14b3fe 100644 --- a/is/ub7/is7.pdf +++ b/is/ub7/is7.pdf Binary files differ diff --git a/is/ub7/is7.tex b/is/ub7/is7.tex index 4a94703..16d37e1 100644 --- a/is/ub7/is7.tex +++ b/is/ub7/is7.tex @@ -105,13 +105,14 @@ % aber es ist doch gefragt wann W unabhängig von X ist $W=-4V-0.5X+0.5N_y+2\alpha X+2N_z+N_w$\\ for $\alpha =0.25$\\ - $W=-4V+0.5N_y+2N_z+N_w$ + $W=-4V+0.5N_y+2N_z+N_w$ \item \begin{align*} \frac{d}{dx}\mathds{E}\left(W|do\ X=x\right)&=-4\frac{d\mathds{E}(V|do\ X=x)}{dx}+0.5\frac{d\mathds{E}(Y|do\ X=x)}{dx}+2\frac{d\mathds{E}(Z|do\ X=x)}{dx}\\ &=0.5\cdot\left(-1\right)+2\cdot\alpha\\ &=2\alpha -0.5 \end{align*} - This is the slope of $W(x)$, which is only depending on $\alpha$. + This is the slope of $W(x)$, which is only depending on $\alpha$.\\ + \textcolor{red}{For large $\alpha$ the influence of X on W is larger} \end{enumerate} \end{document} diff --git a/mr/ubB/mrB.pdf b/mr/ubB/mrB.pdf index eb58472..81558bf 100644 --- a/mr/ubB/mrB.pdf +++ b/mr/ubB/mrB.pdf Binary files differ diff --git a/mr/ubB/mrB.tex b/mr/ubB/mrB.tex index 5de5be7..7b842e5 100644 --- a/mr/ubB/mrB.tex +++ b/mr/ubB/mrB.tex @@ -93,5 +93,18 @@ \item $((s,0))\rightarrow s: ((b,1),(e,1))\rightarrow b: ((e,1),(a,2),(c,7))\rightarrow e: ((a,2),(g,2),(c,7),(f,7)) \\\rightarrow a:((g,2),(c,5),(f,7))\rightarrow g: ((h,3),(c,5),(f,7),(z,8))\\\rightarrow h:((z,4),(c,5),(f,7))\rightarrow (z,4), path=(s,e,g,h,z)$ \item $(s,0+2)\rightarrow s:((e,1+1),(b,1+3))\rightarrow e:((g,2+0),(b,1+3),(f,7+1))\\\rightarrow g:((b,1+3),(h,3+1),(z,8+0))\rightarrow b:((h,3+1),(a,2+4),(z,8+0),(c,7+3))\\\rightarrow h:((z,4+0),(a,2+4),(c,7+3))\rightarrow z: path=(s,e,g,h,z)$ \end{enumerate} + \Aufgabe{Nonholonomic Constraints}{4} + \begin{enumerate}[(a)] + \item $\vec{q}=\begin{pmatrix} + x\\y\\\theta + \end{pmatrix}, f(t,\vec{q},\dot{\vec{q}})=\begin{pmatrix} + 0&1&0 + \end{pmatrix}q(t)-\begin{pmatrix} + 0&1&0 + \end{pmatrix}q(t+1)=\begin{pmatrix} + 0&1&0 + \end{pmatrix}\dot\vec q=0$ + \item nonholonomic, because the derivative of q is used + \end{enumerate} \end{document}