University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg1

EGM6321 - Principles of Engineering Analysis 1, Fall 2009

Mtg 1: Tue, 25 Aug 09

Page 1-1

1-1 defined as (Meeting Number) - (Slide Number)
German Transrapid Emsland 500 km/h , youtube, Uploaded by TransrapidSupporter on Feb 14, 2007
Vu-Quoc & Olson (1989) CMAME
The magnet (i.e vehicle) and structure (i.e. guideway) interaction is shown below.




Where:
$y^1(t)=$ nominal motion
$u^1(s,t)=$ axial displacement of guideway
$u^2(s,t)=$ transversal displacement of guideway

Page 1-2

$f(y^1(t),t)$
Total time derivative of f is given as:

$\begin{array}{c}\frac{d}{dt}f(y^1(t),t)=\frac{\partial f}{\partial s}(y^1(t),t){\dot{y}}^1(t)+\frac{\partial f}{\partial t}(y^1(t),t)\end{array}$

Where ${\dot{y}}^1(t)=\frac{d}{dt}{y}^1(t)$
$\frac{d}{dt}f=f_{,s}(y^1,t){\dot{y}}^1+f_{,t}(y^1,t)$

$\begin{array}{c}\frac{d^2}{d{t}^2}f=f_{,s}(y^1,t){\ddot{y}}^1+f_{,ss}(y^1,t)({\dot{y}}^{\text{'}})+2f_{,st}(y^1,t){\dot{y}}^1+f_{,tt}(y^1,t)\end{array}$

Where ${\dot{y}}^{\text{'}}={\dot{y}}^2$
Coriolis forces - Dynamics

Material time derivative - Continuum Mechanics

Reynolds transport theorem - Continuum Mechanics

$\begin{array}{c}{c}_3(y^{\prime },t){\ddot{y}}^1+c_2(y^1,t)({\dot{y}}^1{)}^2+c_1(y^1,t){\dot{y}}^1+c_0(y^1,t)=0\end{array}$

is an example of a nonlinear ordinary differential equation (ODE)

References

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