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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
