User:EGM6321.f10.team1.Zhichao Gong/Mtg2

Mtg 2: Thu, 27 Jan 11


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page2-1

$${ \color{blue} {P.1-3,}} \ {\color{red}{Eq. (2)}} \ : f=u^{'} \ or \ u^{2} \ {\color{red} (1)}$$

$$Dynamics \ : \ F=m \underset{ \underset{accel \rightarrow { { \overset{}{u}}^{1} \ and \ { \overset{}{u}}^{2} \ and \ { \overset{''}{Y}}^{1} }}{ \uparrow}}{a}$$

HW*: Derive(3)-(4) p.1-3 *:Improvements over existing solution on course wiki: - Better explanations, figures etc. - Theoretical background related to problem -(4)p.1-3: similar to  Coriolis force Dynamics Reynold(Material Time derivate) Transport Thm <P>                                                          Continum Mech</P> <P>(heat, solids, fluids, electronag)</P> <P>Similarities and differences Montesquieu</P> <P>Equation of motion (EOM) of wheel/magnet</P> <P> </P> <P> </P>

$${\color{blue} \underset{c_{3}:{\color{red}mass} \ this \ term \ is  \ N2-ODE}{ \underbrace}}+c_{2}(Y^{'},t){\color{red} { \left( {\color{black}{ \overset{'}{Y}}^{1} }\right)}^{2}}+c_{1}(Y^{'},t){ \overset{'}{Y}}^{1}+{\color{blue} \underset{ \underbrace}}=0 \ {\color{red}(3)}$$

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$${\color{blue}\underline {Note:}} \ Terms \ with \ { \overset{'}{Y}}^{1} \ are \  \underset{not} \ due \ to damping \ {\color{,}} \ but \ to \ {\color{blue}\underline \ {\color{black}convection}}$$

$${\color{blue}Ref: \ VQ4O \ 1989 \ CMAME \ {\color{red}Eqs \ (2.1 \ bc)}}$$

$${\color{blue} \underset{"There \ exists "}{ \underbrace}} \ a \ mispring \ in \ {\color{red}(2.16)}$$

$$c_{0}(Y^{1},t)=-{\color{green} \overset{(A)}{ \overbrace}}-F^{2}u^{2}_{,s}- \frac{T}{R}+ \underset{M}{\color{red}[{\color{black}[1- \overset{-}{R}u^{2}_{,ss}][u^{'}_{,tt}- \overset{-}{R}u^{2}_{,stt}]+u^{2}_{,s}u^{2}_{,tt}}]} \ {\color{red}(1)}$$

From (3) p.2-1:-c<SUB>0</SUB> = horizontal force acting on wheel and magnet

$${\color{green}(A)} \ := \F^{1}[1-\overset{-}{R}u^{2}_{,ss}]$$

$${\color{blue}Dimen Anal:} \ {\color{blue} \underset{ \overset{ \uparrow}{"dimens.  \ of"}}}=F \ {\color{blue}(force)}$$