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x = Ω cos ' Ω = p x + y y = Ω ' ' = arctan (y/x) z = z z = z

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[

\
]
3!,",]
!
"
X!
X"
X
]
[
\
]
3
!
"
G!
!G"
G]
!G"
G"
G"
U
x = cos =

x
2
+ y
2
y = = arctan(y/x)
z = z z = z
u

= cos u
x
+ u
y
u

= u
x
+ cos u
y
u
z
= u
z
r = u

+ zu
z
dr = dl

+ dl

+ dl
z
u
z
= du

+ du

+ dzu
z
dS

= dl

dl
z
= ddz ; dS

= dl

dl
z
= ddz ; dS
z
= dl

dl

= dd
d = dl

dl

dl
z
= dddz
[
\
]
3
U sin !
"
X
U
X"
X
!
!
U cos !
[
\
]
3
"
!
U sin ! G"
U
G!
G"
U G!
U sin ! G"
U
G"
GU
x = r cos r =

x
2
+ y
2
+ z
2
y = r = arctan(

x
2
+ y
2
/z)
z = r cos = arctan(y/x)
u
r
= cos u
x
+ u
y
+ cos u
z
u

= cos u
x
+ u
y
u
z
u

= u
x
+ cos u
y
r = ru
r
dr = dl
r
u
r
+ dl

+ dl

= dru
r
+ rdu

+ r du

dS
r
= dl

= r
2
dd; dS

= dl
r
dl

= r drd; dS

= dl
r
dl

= rdrd
d = dl
r
dl

= r
2
drdd
f = f(x, y, z) A(x, y, z) = A
x
(x, y, z)u
x
+A
y
(x, y, z)u
y
+
A
z
(x, y, z)u
z
f =
f
x
u
x
+
f
y
u
y
+
f
z
u
z
A =
A
x
x
+
A
y
y
+
A
z
z
A =

A
z
y

A
y
z
!
u
x
+

A
x
z

A
z
x
!
u
y
+

A
y
x

A
x
y
!
u
z
(f)
2
f =

2
f
x
2
+

2
f
y
2
+

2
f
z
2
f = f(, , z) A(, , z) = A

(, , z)u

+A

(, , z)u

+
A
z
(, , z)u
z
f =
f

+
1

+
f
z
u
z
A =
1

(A

+
1

+
A
z
z
A =

A
z

z
!
u

z

A
z

!
u

+
1

(A

!
u
z

2
f =
1

!
+
1

2
f

2
+

2
f
z
2
f = f(r, , ) A(r, , ) = A
r
(r, , )u
r
+ A

(r, , )u

+
A

(r, , )u

f =
f
r
u
r
+
1
r
f

+
1
r
f

A =
1
r
2
(r
2
A
r
)
r
+
1
r
( A

+
1
r
A

A =
1
r

( A

!
u
r
+
1
r

A
r


(rA

)
r
!
u

+
1
r

(rA

)
r

A
r

!
u

2
f =
1
r
2

r
2
f
r
!
+
1
r
2

!
+
1
r
2 2

2
f

2
A B C
A (BC) = B (CA) = (AB) C
A(BC) = B(A C) C(A B)
f = f(r) g = g(r) A = A(r) B = B(r)
(f + g) = f +g
(fg) = f(g) + g(f)
(A+B) = A+ B
(fA) = f( A) +A (f)
(AB) = B (A) A(B)
(A+B) = A+B
(fA) = f(A) A(f)
(A) = 0
(f) = 0
(A) = ( A)
2
A

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