diff --git a/mr/ubC/assignment12.pdf b/mr/ubC/assignment12.pdf new file mode 100644 index 0000000..f55588f --- /dev/null +++ b/mr/ubC/assignment12.pdf Binary files differ diff --git a/mr/ubC/mrC.pdf b/mr/ubC/mrC.pdf new file mode 100644 index 0000000..453d24b --- /dev/null +++ b/mr/ubC/mrC.pdf Binary files differ diff --git a/mr/ubC/mrC.tex b/mr/ubC/mrC.tex new file mode 100644 index 0000000..8ee214a --- /dev/null +++ b/mr/ubC/mrC.tex @@ -0,0 +1,127 @@ +\documentclass[a4paper,12pt]{scrartcl} +\usepackage[ngerman]{babel} +\usepackage{graphicx} %BIlder einbinden +\usepackage{amsmath} %erweiterte Mathe-Zeichen +\usepackage{amsfonts} %weitere fonts +\usepackage[utf8]{inputenc} %Umlaute & Co +\usepackage{hyperref} %Links +\usepackage{ifthen} %ifthenelse +\usepackage{enumerate} +\usepackage{pdfpages} +\usepackage{algpseudocode} %Pseudocode +\usepackage{dsfont} % schöne Zahlenräumezeichen +\usepackage{amssymb, amsthm} %noch stärker erweiterte Mathe-Zeichen +\usepackage{tikz} %TikZ ist kein Zeichenprogramm +\usetikzlibrary{trees,automata,arrows,shapes} +\usepackage{qtree} +\usepackage{listings} +\lstset{language=Matlab} + +\pagestyle{empty} + + +\topmargin-50pt + +\newcounter{aufgabe} +\def\tand{&} + +\newcommand{\makeTableLine}[2][0]{% + \setcounter{aufgabe}{1}% + \whiledo{\value{aufgabe} < #1}% + {% + #2\tand\stepcounter{aufgabe}% + } +} + +\newcommand{\aufgTable}[1]{ + \def\spalten{\numexpr #1 + 1 \relax} + \begin{tabular}{|*{\spalten}{p{1cm}|}} + \makeTableLine[\spalten]{A\theaufgabe}$\Sigma$~~\\ \hline + \rule{0pt}{15pt}\makeTableLine[\spalten]{}\\ + \end{tabular} +} + +\def\header#1#2#3#4#5#6#7{\pagestyle{empty} +\begin{minipage}[t]{0.47\textwidth} +\begin{flushleft} +{\bf #4}\\ +#5 +\end{flushleft} +\end{minipage} +\begin{minipage}[t]{0.5\textwidth} +\begin{flushright} +#6 \vspace{0.5cm}\\ +% Number of Columns Definition of Columns second empty line +% \begin{tabular}{|*{5}{C{1cm}|}}\hline A1&A2&A3&A4&$\Sigma$\\\hline&&&&\\\hline\end{tabular}\\\vspace*{0.1cm} +\aufgTable{#7} +\end{flushright} +\end{minipage} +\vspace{0.5cm} +\begin{center} +{\Large\bf Assignment #1} + +{(Hand-in date #3)} +\end{center} +} + + + +%counts the exercisenumber +\newcounter{n} + +%Kommando für Aufgaben +%\Aufgabe{AufgTitel}{Punktezahl} +\newcommand{\Aufgabe}[2]{\stepcounter{n} +\textbf{Exercise \arabic{n}: #1} (#2 Punkte)} + +\newcommand{\Normal}[3]{\mathcal{N}\left(#1,#2,#3\right)} +\newcommand{\Normalf}[3]{\frac{\left|#3\right|^{-\frac{1}{2}}}{\sqrt{2\pi}}e^{-\frac{\left(#1 - #2 \right)^2\cdot \left(#3\right)^{-1}}{2}}} + +\begin{document} + %\header{BlattNr}{Tutor}{Abgabedatum}{Vorlesungsname}{Namen}{Semester}{Anzahl Aufgaben} + \header{12}{}{2015-07-21}{Mobile Robots}{ + \textit{Jan-Peter Hohloch}\\ \textit{Maximus Mutschler} + }{SS 15}{3} + \vspace{0.2cm} + \Aufgabe{Moment of Inertia}{6} + \begin{enumerate}[(a)] + \item $I=m_c\begin{pmatrix} + 0&0&0\\0&0&0\\0&0&0 + \end{pmatrix}+m_m\left(\begin{pmatrix} + 0&0&0\\0&0.04&0\\0&0&0.04 + \end{pmatrix}+\begin{pmatrix} + 0.04&0&0\\0&0&0\\0&0&0.04 + \end{pmatrix}\right.\\\left.+\begin{pmatrix} + 0&0&0\\0&0.04&0\\0&0&0.04 + \end{pmatrix}+\begin{pmatrix} + 0.04&0&0\\0&0&0\\0&0&0.04 + \end{pmatrix}\right)\\=0.2kg\cdot m^2\begin{pmatrix} + 0.08&0&0\\0&0.08&0\\0&0&0.16 + \end{pmatrix}$ + \item $I=m_c\begin{pmatrix} + 0&0&0\\0&0&0\\0&0&0 + \end{pmatrix}+m_m\left(\begin{pmatrix} + 0.02&0.02&0\\0.02&0.02&0\\0&0&0.04 + \end{pmatrix}+\begin{pmatrix} + 0.02&-0.02&0\\-0.02&0.02&0\\0&0&0.04 + \end{pmatrix}\right.\\\left.+\begin{pmatrix} + 0.02&0.02&0\\0.02&0.02&0\\0&0&0.04 + \end{pmatrix}+\begin{pmatrix} + 0.02&-0.02&0\\-0.02&0.02&0\\0&0&0.04 + \end{pmatrix}\right)\\=0.2kg\cdot m^2\begin{pmatrix} + 0.08&0&0\\0&0.08&0\\0&0&0.16 + \end{pmatrix}$\\ + The result is the same, that however isn't very suprising since the Moment of Inertia should be independent of the rotation around the z-axis. %TODO: really? + \end{enumerate} + \Aufgabe{Hexacopter}{8} + \begin{enumerate}[(a)] + \item $^Bp_1=\begin{pmatrix} + 1\\0\\0 + \end{pmatrix}l,\ ^Bp_2=\begin{pmatrix} + \frac{1}{2}\\\frac{\sqrt{3}}{2}\\0 + \end{pmatrix}l,\ ^Bp_3=\begin{pmatrix} + -\frac{1}{2}\\\frac{\sqrt{3}}{2}\\0 + \end{pmatrix}l$ + \end{enumerate} +\end{document} +