User:Egm6321.f10.team4.Yoon/Mtg2

=EGM6321 - Principles of Engineering Analysis 1, Fall 2010=

 Mtg 2: Thu, 26 Aug 10

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[[media:2010_08_24_15_22_30.djvu | Eqs.(2), p.1-3]]: $$\displaystyle f=u^1 $$ or $$\displaystyle u^2$$ (1)

Dynamics: $$\displaystyle F=m \cdot a$$ (2) with the accereration $$\displaystyle a $$ could be one of the following quantities $$\displaystyle \ddot u^1, \ddot u^2, or, \ddot Y^1$$

Next, equations of motion.

= Equation of motion(EOM) of wheel/Magnet =

N2_ODE

[[media: 2010_08_26_13_57_13.djvu | Page 2-2]]
Note: Terms with $$\displaystyle \dot Y^1$$ are not due to damping, but to convection.

Ref:VQ&O 1989 CMAME Eqs(2.1bc) $$\displaystyle \ \ \exists $$(There exists) a misprint in (2.1b)

where, M is mass of wheel/magnet

From Eqs.[[media: 2010_08_24_15_22_30.djvu | (3),p.2-1]]: $$\displaystyle c_0$$ is horizontal force acting on wheel/magnet

$$\displaystyle A:=F^1[1-\bar R u^2_{,SS}]$$

Dimensional Analysis
$$\displaystyle \underbrace{[F^1]}_{\color{blue}{_{dimension of}}}=F_{(force)}$$

[[media: 2010_08_26_13_57_13.djvu | Page 2-3]]
where the number 2 in $$\displaystyle \partial^2 $$ means the 2nd derivative; the number 2 in $$\ \displaystyle U^2 $$ means the superscript, and the number 2 in $$\ \displaystyle \partial S^2 $$ means the power (i.e., $$\displaystyle (\partial S)^2$$).