d
dx
∂f
∂y
′
i
−
∂f
∂y
i
= 0, i = 1, 2, ..., s. (9.3)
a b
t
1
A
q
(1)
1
, q
(1)
2
, . . . , q
(1)
s
t
2
B
q
(2)
1
, q
(2)
2
, ..., q
(2)
s
q
i
(t)
S =
t
2
Z
t
1
L (q
1
(t), . . . , q
s
(t), ˙q
1
(t), . . . , ˙q
s
(t), t) dt (9.4)
S
δS =
s
X
i=1
t
2
Z
t
1
∂L
∂q
i
−
d
dt
∂L
∂ ˙q
i
δq
i
dt = 0. (9.5)
S
δq
i
(t
1
) = δq
i
(t
2
) = 0 , i = 1, 2, . . . , s .