AN INTRODUCTION TO SONA
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R SYSTEMS ENGINEERING
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SECOND EDITION g
LAWRENCE J. ZIOMEK g g
Complete Chapter Solutions Manual are
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included (Ch 1 to 15)
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** Immediate Download
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** Swift Response
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** All Chapters included
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, Chapter 1
g
Sectiong1.2
1-1 Verifyg(1.2-12)gandg(1.2-13).
rggr0g g g g g
g g g g g g
g g g
2
r gr0 g2(rg r0g)
2
Sinceg rgg rg ,g r0g g r0g ,gandg rggrrˆg,gthen
rggr0g rg2grg02g2r(grˆ•grg0)
r02 g
r g1ggg 2ggg2g
2
r r 0
gr 1ggb
grg g2 rˆ•gr
whereg bgg 0
g2g 0g
g rg
g g
r
1
,1-2 UsinggFig.gP1-2,gshowgthat
uggcosg gsingcosg ,
vggcosgggsingsing ,
and
wggcosg gcosg ,
whereg ug,g vg,gandg wg aregdimensionlessgdirectiongcosinesgwithgrespectgtogtheg Xg,g Yg,gandg Z
axes,grespectively.
Z
(r, , )
r
Y
X
FiguregP1-2
2
, Z
rgsin
(r, , )
r
Y
rgsin
X
r rgsin
rgcosg rgcosg
X X
grgcos
cosg
rgsin
uggsingcosg gcos
3