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\documentclass[12pt]{article} % BB Feb 22 2009. \usepackage{epsfig} \textheight 9.0in \textwidth 6.0in \topmargin -0.4in \headsep 0.4in \oddsidemargin 0.25in \evensidemargin 0.25in \def\sqr#1#2{{\vcenter{\hrule height.#2pt \hbox{\vrule width.#2pt height#1pt \kern#1pt \vrule width.#2pt} \hrule height.#2pt}}} \def\square{{\mathchoice\sqr64\sqr64\sqr{4.2}3\sqr{3.0}3}} \def\undertext#1{$\underline{\smash{\hbox{#1}}}$} \pagestyle{empty} \begin{document} \begin{center} {\bf ADVANCED DYNAMICS --- PHY 4241/5227}\\\vspace {2mm} {\bf SOLUTIONS -- SET 9}\\% \vspace {3mm} (February 25, 2009) \\ \end{center} \setcounter{equation}{0} \begin{description} \item{(41.1)} $$\frac{1}{\sqrt{1-\tanh^2(\zeta)}} = \sqrt{\frac{\cosh^2(\zeta)} {\cosh^2(\zeta)-\sinh^2(\zeta)}} = \cosh(\zeta)\ .$$ \item{(41.2)} $$\cosh(\zeta_1)\,\cosh(\zeta_2)+\sinh(\zeta_1)\,\sinh(\zeta_2)$$ $$=\frac{e^{\zeta_1}+e^{-\zeta_1}}{2}\,\frac{e^{\zeta_2}+e^{-\zeta_2}}{2} This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: + \frac{e^{\zeta_1}-e^{-\zeta_1}}{2}\,\frac{e^{\zeta_2}-e^{-\zeta_2}}{2}$$ $$=\frac{e^{\zeta_1+\zeta_2}+2\,e^{\zeta_1-\zeta_2}+e^{-\zeta_1-\zeta_2}}{4} + \frac{e^{\zeta_1+\zeta_2}-2\,e^{\zeta_1-\zeta_2}+e^{-\zeta_1-\zeta_2}}{4}$$ $$= \cosh(\zeta_1+\zeta_2)$$ \item{(41.3)} \begin{eqnarray} \nonumber \tanh(\zeta_1+\zeta_2) &=& \frac{\sinh(\zeta_1+\zeta_2)} {\cosh{\zeta_1+\zeta_2}} \\ \nonumber &=&\frac{\sinh(\zeta_1)\,\cosh(\zeta_2)+\cosh(\zeta_1)\,\sinh(\zeta_2)} {\cosh(\zeta_1)\,\cosh(\zeta_2)+\sinh(\zeta_1)\,\sinh(\zeta_2)} \\ \nonumber &=&\frac{\tanh(\zeta_1)+\tanh(\zeta_2)} {1+\tanh(\zeta_1)\,\tanh(\zeta_2)} \ =\ \frac{\beta_1+\beta_2}{1+\beta_1\,\beta_2} \end{eqnarray} \end{description} % \begin{figure}[tb] \vspace{5pc} % \centerline{\hbox{ \psfig{figure=figs/ladder.eps,width=7.5cm} }} % \caption{Ladder for assignment~14.} \label{fig_lader} \end{figure} \end{document}...
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This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.

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