AN INTRODUCTION TO SON
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AR SYSTEMS ENGINEERING
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SECOND EDITION y
LAWRENCE J. ZIOMEK y y
Complete Chapter Solutions Manualare
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included (Ch 1 to 15)y y y y
** Immediate Download
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** Swift Response
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** All Chapters included
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, Chapter 1
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Sectiony1.2
1-1 Verifyy(1.2-12)yandy(1.2-13).
ryyr0y (ryyr0y)•(ryyr0y)
ry•(ryyr0y)yyr0y•y(ryyr0y)
ry•yryyry•yr0y yr0y •yryyr0y •yr0
2
r y r0y y y2(ry•yr0y)
2
Sincey ryy ry ,y r0y y r0y,yandy ryyrrˆy,ythen
ryyr0y ryy2 yryy02y2r(yr̂ •yryy)0
r02 r̂ •yryy0
r y1yy 2y y2
2
r r
yr 1yyb
yry y2 r̂ •yr
wherey byyy y 0y y2 0y
y ry
y
r
1
,1-2 UsingyFig.yP1-2,yshowythat
uyycosy ysinycosy ,
vyycosyy ysinysiny ,
and
wyycosy ycosy ,
wherey uy,y vy,yandy wy areydimensionlessydirectionycosinesywithyrespectytoythey Xy ,y Yy,yandy Z
axes,yrespectively.
Z
(r,y , )
r
Y
X
FigureyP1-2
2
, Z
rysin
(r,y , )
r
Y
rysin
X
r rysin
rycos rycos
X X
rycosy
cosy
rysin
uyysinycosy ycos
3