Geodetic Mapping - Map Projections: Cartographic Information Systems - page 504

sin B 0 b +O C ( b 2 ) ,

cos B =cos( B 0 + b )=cos B 0 −

E 2 sin 2 B 2 ) − 2 =1+2 E 2 sin 2 B +O( E 4 )=
= 1+2 E 2 sin B 0 +4 E 2 sin B 0 cos B 0 +O( E 4 ) b +O( b 2 ) ,

(1 −

(20.168)

E 2 sin 2 B ) − 2 = cos B (1 −

sin B 0 b +2 E 2 sin 2 B 0 cos B 0 2 E 2 sin 3 B 0 b +4 E 2 sin B 0 cos 2 B 0 b +O( b 2 ) ,

B S = B 0 + b S ,B N = B 0 + b N ,

=cos B 0 − −

+ l E b N

= A 1 (1 E 2 ) d b (cos B 0 +2 E 2 sin 2 B 0 cos B 0 )+

S E 2 A 1 ,A 2 − d l (20.169)

−l E b S

+ l E b N

+ A 1 (1 E 2 ) 2 E 2 sin 3 B 0 +4 E 2 sin B 0 cos 2 B 0 + o ( E 4 )] b +O( b 2 ) ,

− d l d b [ − sin B 0 −

−l E b S

E 2 ) l E 2(cos B 0 +2 E 2 sin 2 B 0 cos B 0 )( b N − = A 1 (1 S E 2 A 1 ,A 2 − b S )+ (20.170)

+[ − sin B 0 − 2 E 2 sin 3 B 0 +4 E 2 sin B 0 cos 2 B 0 +O( E 4 )]( b N − b S )+O( b N − b S ) ,

+ l E b N

d b cos B 0 +2 E 2 sin 2 B 0 cos B 0 + I AR = A 1 (1

E 2 )
2 S E 2 A 1 ,A 2

−

d l

−l E b S

2 E 2 sin 3 B 0 +4 E 2 sin B 0 cos 2 B 0 cos 2 B 0 +O( E 4 )] b +O( b 2 ) × +[ − sin B 0 − (20.171)

cos 4 B 0
36

(1 − E 2 sin 2 B 0 ) 2 b 4 +O R ( l 5 ,b 5 ) ,

E 2 sin 2 B 0 ) 2
(1

l 4 + cos 2 B 0
18

E 2 ) 2

(1 −

l 2 b 2 + 1
36

(1 −

×

− E 2 ) 2

+ l E b N

I AR = A 1 (1

E 2 )
2 S E A 1 ,A 2

−

d b [ Al 4 + Bl 2 b 2 + Cb 4 + Dl 4 b + Pl 2 b 3 d l

−l E b S

+ Qb 5 +O R (6)] ,

(20.172)

(1 − E 2 sin 2 B 0 ) 2
(1

A := [cos B 0 +2 E 2 sin 2 B 0 cos B 0 +O( E 4 )] cos 4 B 0
36

,

− E 2 ) 2

B := [cos B 0 +2 E 2 sin 2 B 0 cos B 0 +O( E 4 )] cos 2 B 0 ,

18

E 2 ) 2

C := [cos B 0 +2 E 2 sin 2 B 0 cos B 0 +O( E 4 )] 1
36

(1 −

E 2 sin 2 B 0 ) 2 , (1 −

(20.173)

sin B 0 cos 4 B 0
36

D := − [3 + 2 E 2 (3 cos 2 B 0 )] + O( E 4 ) , −