108
DOC.
1
MECHANICS LECTURE
NOTES
+
B2{(p'2
sin2
ß
+
(a'
+
p'
cosß)2}
a'2 +
2tx'(p'cosß}
p
der Reihe nach
gleich
a,
ß &
(p
gesetzt
2
L
=
A(a'
+
cp
cosß)2
+
B(ß'2
+
(p'2sin2ß)212
d
(dL\
d
,
"-ish""
+
",cosW,
o o
*
0
=
!2ß"'i
0
=
dt
\dp'
=V-{2i4(a'
+ (p'cosß)cosß +
25sin2/?jp'}
^
=
0
~
=
2B(p'2
sii^ßcos ß
~
=
0
da
Also
werden die
Gleichungen
von
Lagrange
{a'
+ (p'cosßi
=
0
d_
Jt
{ß'}
-
p'2
sin
ß cos ß
=
0
d_
Jt
{A(a'
+
jp'cos/?)cos/?
+
B
sin2
ßcp'} =
0
[p. 100]
2L
=
A{a'
+
cp'
cos
ß)2
+
B{ß'2
+
(p'2
sin2
ß)
dL
dct
-
=
A(a'
+
cp'cosß)
dL
da.
=
0
dL
dß
,
=
Bß'
dL
dß
=
-
A(a'
+
/cos/?)j9'sin/J
dL
+
B(p'2
sin
ß
cos
ß
d(p
-
=
A(a'
+
q'cosß)
cosß
+
Bcp'
sin2 ß
dL
dcp
=
0