msolution1 - % BB Mar 10 2010...

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% BB Mar 10 2010 \documentclass[12pt]{article} \textheight 9.5in \textwidth 6.0in \topmargin -0.7in \headsep 0.4in \oddsidemargin 0.25in \evensidemargin 0.25in \def\pmbf#1{{\mbox{\boldmath${#1}$}}} \def\undertext#1{$\underline{\smash{\hbox{#1}}}$} \pagestyle{empty} \begin{document} %----------------------------------------------------% %%%%%%%%%%%%%%%%% ADVANCED DYNAMICS %%%%%%%%%%%%%%%% %----------------------------------------------------% \begin{center} {\bf SOLUTIONS MIDTERM ADVANCED DYNAMICS --- PHY--4241/5227}\\ \end{center} \setcounter{equation}{0} \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%% \centerline{\bf PROBLEM 1 (20 points)} \begin{enumerate} \item $$ \frac{\partial L}{\partial q_i} = \frac{d~}{dt} \frac{\partial L}{\partial \dot{q}_i}\,,~~~p_i = \frac{\partial L}{\partial \dot{q}_i}\,,~~~ {\rm for}~~~ i=1,\dots,n\,. $$ \item $$ L = \frac{1}{2}\,m\,\dot{x}^2 - \frac{1}{2}\,k\,x^2\,.$$ \item $$ p = \frac{\partial L}{\partial\dot{x}} = m\,\dot{x}\,.$$ \item $$ H = \frac{p^2}{2m} + \frac{1}{2}\,k\,x^2\,.$$ \item $$ \dot{x} = \frac{\partial H}{\partial p} = \frac{p}{m}\,,
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msolution1 - % BB Mar 10 2010...

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