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S
0
(t) = lim
∆t→0
1
2
a cos t b sin t
a cos(t + ∆t) b sin(t + ∆t)
∆t
=
ab
2
lim
∆t→0
sin ∆t
∆t
=
ab
2
.
S(t) =
Z
t
0
S
0
(t) dt =
Z
t
0
ab
2
dt =
ab
2
t.
t
OAM
2
ab
ch t =
1
2
(e
t
+ e
−t
) sh t =
1
2
(e
t
− e
−t
)
ch
2
t − sh
2
t = 1
x
2
a
2
−
y
2
b
2
= 1
x = a ch t, y = b sh t.
A
M
O
t
t
S
0
(t) S(t)
OAM A(a; 0)
M(t)
t
S
0
(t) = lim
∆t→0
1
2
a ch t b sh t
a ch (t + ∆t) b sh (t + ∆t)
∆t
=
ab
2
lim
∆t→0
sh ∆t
∆t
=
ab
2
,
S(t) =
ab
2
t
t
861\
1 a cos t b sin t
S 0 (t) = lim
2 a cos(t + ∆t) b sin(t + ∆t)
=
ab
lim
sin ∆t ab
= . ^^
∆t 2 ∆t→0 ∆t 2
8/JL6
∆t→0
^
Z t Z t
0 ab ab
S(t) = S (t) dt = dt = t.
2 2
610; -+36[-;\ .636;*83 t b 236b,*,09N `` · ~8- -30*,803-b6,,69 .7-K
0 0
}6L? /*18-36 OAM \ b[9869 / 1-~OO0 0*,8-; 2 =
Q0.*3+-70)*/10* O2,1 00 ch t = (e + e ab) 0 sh t = (e − e ) 2L-K
1 t −t 1 t −t
b7*8b-39J8 8-|L*/8b2 ch t − sh t = 1 = 8- 8-|L*/8b- L6*8 b-[;-|,-/8?
2 2
2 2
.636;*830[-b68? .36b2J b*8b? :0.*3+-7
x
−
y
=1
2
2
2
2
^]
a b
/7*L2J}0; -+36[-;
x = a ch t, y = b sh t. ^Æ
Q*-;*830)*/10M /;/7 .636;*836 t b
236b,*,09N ^Æ 6,67-:0)*, :*-;*8K
30)*/1-;2 /;/72 .636;*836 t b 236bK
,*,09N ~770./6 ``= {)0/799 .3-K M
0[b-L,2J S (t) -8 O2,1 00 S(t) \.3*LK
0
/86b79J}*M /-+-M .7-}6L? /*18-36 O A
OAM \:L* A(a; 0) · b*3I0,6 :0.*3+-K
7\ 6 M (t) · 8-)16 :0.*3+-7\ -.3*K
L*79*;69 /--8b*8/8b2J}0; [,6)*,0K
*; .636;*836 t \ 6,67-:0),- /72)6J Ç0/= _^=
~770./6 .-72)0;
1 a ch t b sh t
S 0 (t) = lim
2 a ch (t + ∆t) b sh (t + ∆t)
=
ab
lim
sh ∆t ab
= , ^Ú
∆t→0 ∆t 2 ∆t→0 ∆t 2
-812L6 6,67-:0),- ^ .-72)6*; S(t) = ab t = 610; -+36[-;\ .636;*83 t
2
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