User:EGM6321.f09.team1.Zhichao Gong/Mtg2

Mtg 2: Thu, 27 Aug 09

page2-1


 * PEA1.F09.Mtg2.pg1.fig1.svg

p. 1-2, Eqs (1), (2)

f(s,t)

$$S \equiv {X}^{1}= \ axial \ coordinate$$

$$t \ = \ time$$

$$ \begin{cases} & X \ = \ capital \ (uppercase) \\ & x \ = \ small \ (lowercase) \end{cases}$$

$$ \begin{cases} & Y \ = \ uppercase \\ & y \ = \ lowercase \end{cases}$$ $$At \ S={Y}^{1}(t), \ have f({Y}^{1},t) \ and \ time \ t$$ page2-2

HW: Derive Eqs (1), (2) p.1-2 Montesquieu  

p.1-2Eq(3)       Eq. of motion of wheel(vehicle)

Note: $$\overset{.}{Y}^{1}$$ Math struct of ci</SUB>(Y<SUP>1</SUP>,t) known </P> <P>but values of c<SUB>i</SUB> not known at any t</P> <P>terms not due to damping,</P> <P>but due to chain rulel called</P> <P><U>"convective terms"</U></P>

<P>Similarly for</P>

$${c}_{i}({Y}^{1},t), \ i=1,2,3$$

<P>Note: Math struct of c<SUB>i</SUB>(Y<SUP>1</SUP>,t) known </P> <P>but values of c<SUB>i</SUB> not known at any t</P>

page2-3

Since \ $${\color{red} \left\{ {\color{black}{Y}^{1} \ {u}^{1} \ {u}^{2}}\right\}}$$

are unknown functions to be solved for.

<P>There are 2 more equations of motion for</P> <P>u<SUP>1</SUP>(s,t) and u<SUP>2</SUP>(s,t)</P> $${\color{red} \Rightarrow \ PDEs}$$

<P><U>Note:</U> Result is a set of coupled,</P> <P>nonlinear ODE and PDEs</P>

Simplify:

<P>2nd order to 1st order</P> <P>nonlinear to linear</P> <P>unknown varying coefficient to known varying coefficient</P>