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°
O
A t r
r O A
r A
r(t) r(t)
r(t)
B s
A
s
A B
s r(s)
τττ
ττ
=
dr
ds
. (1.1)
τττ
ττ
(τττ
ττ
, τττ
ττ
) = 1 (1.2)
τττ
ττ
K =
dτττ
ττ
ds
=
d
2
r
ds
2
, (1.3)
n
K =
dτττ
ττ
ds
= Kn =
1
ρ
n, K =
1
ρ
. (1.4)
K ρ
C n
C τττ
ττ
n
0 =
d
ds
(τττ
ττ
, τττ
ττ
) = 2(
dτττ
ττ
ds
, τττ
ττ
) = 2(K, τττ
ττ
) = 2
1
ρ
(n, τττ
ττ
).
b τττ
ττ
n b
b = [τττ
ττ
, n]
r(t)
r(s) s(t)
V =
dr
dt
=
˙
r. (1.5)
V =
dr
dt
=
dr
ds
ds
dt
= τττ
ττ
ds
dt
= V τττ
ττ
, (1.6)
V
t
V =
ds
dt
. (1.7)
a(t)
A B
a(t) = AB
da
dt
=
˙
a = V
B
− V
A
. (1.8)
¤ O
r
A
r
B
A B
a = r
B
− r
A
, ˙a = ˙r
B
− ˙r
A
= V
B
− V
A
. ¥
W =
dV
dt
=
˙
V =
d
2
r
dt
2
=
¨
r. (1.9)
W =
dV
dt
=
d(V τττ
ττ
)
dt
=
dV
dt
τττ
ττ
+ V
dτττ
ττ
dt
.
dτττ
ττ
dt
=
dτττ
ττ
ds
ds
dt
=
n
ρ
V
W =
dV
dt
τττ
ττ
+
V
2
ρ
n = W
τ
+ W
n
: (1.10)
W
W
τ
W
n
W
τ
=
dV
dt
, W
n
=
V
2
ρ
. (1.11)
τττ
ττ
n
W
2
= W
2
τ
+ W
2
n
. (1.12)
O A
1
A
2
A
3
i
k
= OA
k
(i
k
, i
l
) = δ
kl
=
½
1, k = l,
0, k 6= l.
(2.1)
x
k
= (r, i
k
r = OB i
k
: r =
3
P
k=1
x
k
i
k
x
1
x
2
x
3
