MANUAL for An u u u
Introduction to So u u
nar Systems Engi
u u
neering, 2e by Law
u u u
rence J.u
Ziomek (Al u
l Chapters)
u
, Chapter 1
u
Sectionu1.2
1-1 Verifyu(1.2-12)uandu(1.2-13).
ruur0u (ruur0u)•(ruur0u)
ru•(ruur0u)uur0u•u(ruur0u)
ru•uruuru•ur0u ur0u •uruur0u •ur0
2
r u r0u u u2(ru•ur0u)
2
Sinceu ruu ru ,u r0u u r0u,uandu ruurrˆu,uthen
ruur0u ruu2 uruu02u2r(ur̂ •uruu0)
r2 r̂ •uruu0
r2u1uu 02u u2
r r
ur 1uub
uru u2 r̂ •ur
whereu buuu u 0u u2 0u
u ru
u
r
1
,1-2 UsinguFig.uP1-2,ushowuthat
uuucosu usinucosu ,
vuucosuu usinusinu ,
and
wuucosu ucosu ,
whereu uu,u vu,uandu wu areudimensionlessudirectionucosinesuwithurespectutoutheu Xu,u Yu,uandu Z
axes,urespectively.
Z
(r,u , )
r
Y
X
FigureuP1-2
2
, Z
rusin
(r,u , )
r
Y
rusin
X
r rusin
rucos rucos
X X
rucosu
cosu
rusin
uuusinucosu ucos
3