Solutions Manual For An Introduction to Sonar Systems Engineering 2nd Edition By Lawrence J. Ziomek (All Chapters)

SOLUTIONS
MANUAL for An Y Y Y




Introduction to So Y Y




nar Systems Engi
Y Y




neering, 2e by La
Y Y Y




wrence J. Y




Ziomek (Al Y




l Chapters)
Y

, Chapter 1
Y




SectionY1.2

1-1 VerifyY(1.2-12)YandY(1.2-13).

rYYr0Y (rYYr0Y)•(rYYr0Y
 )rY•(rYYr Y)YYr Y•Y(rYYr Y
0 0 0

 )rY•YrYYrY•Yr0Y Yr0Y •YrYYr0Y •Y
 r0 2 2
 r
 Y r0Y Y Y2(rY•Yr0Y
SinceY rYY r)Y ,Y r0Y Y r0Y,YandY rYYrrˆY,Ythen


rYYr0Y rYY2 Yr0YY2 Y2r(Yr̂ •Yr0YY
 )
 r2 r̂ •YrYY
0 
 r2Y1YY 20Y Y
2 
 r r 
Yr 1YY
b
YrY Y2 r̂ •Yr
whereY bYYY Y 0Y Y2 0Y
Y rY 

Y



r




1

,1-2 UsingYFig.YP1-2,YshowYthat

uYYcosY YsinYcosY ,

vYYcosYY YsinYsinY ,

and
wYYcosY YcosY ,

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 
rYcosY
cosY 
rYsin
uYYsinYcosY Ycos




3