MANUAL for An I J J J
ntroduction to Son J J
ar Systems Engine
J J
ering, 2e by Lawre
J J J
nce J. J
Ziomek (Al J
lChapters)
J
, Chapter 1
J
SectionJ1.2
1-1 VerifyJ(1.2-12)JandJ(1.2-13).
rJJr0J J J J J
J J J J J J
J J J
2
r Jr0 J2(rJ r0J)
2
SinceJ rJJ rJ ,J r0J J r0J ,JandJ rJJrrˆJ,Jthen
rJJr0J rJ2JrJ 02 J2r(Jrˆ•JrJ )0
r2 J
r2J1JJJ 0JJ2J2J
r r 0
Jr 1JJb
JrJ J2 rˆ•Jr
whereJ bJJ J 0J J2J 0J
J rJ
r
1
,1-2 UsingJFig.JP1-2,JshowJthat
uJJcosJ JsinJcosJ ,
vJJcosJJJsinJsinJ ,
and
wJJcosJ JcosJ ,
whereJ uJ,J vJ,JandJ wJ areJdimensionlessJdirectionJcosinesJwithJrespectJtoJtheJ XJ,J YJ,JandJ Z
axes,Jrespectively.
Z
(r, , )
r
Y
X
FigureJP1-2
2
, Z
rJsin
(r, , )
r
Y
rJsin
X
r rJsin
rJcosJ rJcosJ
X X
rJ Jcos
cosJ
rJsin
uJJsinJcosJ Jcos
3