User:Egm6321.f09.mtg1

=EGM6321 - Principles of Engineering Analysis 1, Fall 2009= MEETING 1 - Tuesday, 25Aug09

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1-1 defined as (Meeting Number) - (Slide Number) Watch video: Magnetic levitation, Transrapid 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

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$$ f(y^1(t),t) \ $$ Total time derivative of f is given as: EQ1) $$\frac{d}{dt} f(y^1(t),t)= \frac{\partial f}{\partial s}(y^1(t),t) \dot y^1(t)+\frac{\partial f}{\partial t}(y^1(t),t) \ $$ Where $$ \dot y^1(t)=\frac{d}{dt}y^1(t) \ $$ $$ \frac{d}{dt}f=f_{,s}(y^1,t) \dot y^1+f_{,t}(y^1,t) $$  EQ2) $$ \frac{d^2}{dt^2}f=f_{,s}(y^1,t)\ddot y^1+f_{,ss}(y^1,t)(\dot y^')+2f_{,st}(y^1,t) \dot y^1 + f_{,tt}(y^1,t) $$ Where $$ \dot y^'= \dot y^2 $$ Coriolis forces - Dynamics

Material time derivative - Continuum Mechanics

Reynolds transport theorem - Continuum Mechanics EQ3) $$ c_3(y',t) \ddot y^1+c_2(y^1,t) (\dot y^1)^2+c_1(y^1,t) \dot y^1+c_0(y^1,t)=0 $$ is an example of a nonlinear ordinary differential equation (ODE)