DOI Page / Citation link:
https://doi.org/10.11588/diglit.43680#0102
aus Kurven konstanter geodätischer Krümmung
15
IV.
Vcc(ü — ü)4 + 2 ^(z7 — ü)2 + 73
F=
F '
2(ü + y + c).[z??—-^(w —ü)2]rf(« + ü)
a (u — u)(u-\-u-y cY d(u — u)
]/a(zz— ü)4 + 2^(ü—n)2 + y3
Für cz c2 — 4 772 =y 0 ergibt sich:
0
(65) F t
2 !a(u— z?)2— 2 [2/72 — ac(2z + f + c)] z
a(ac2—4772) \ /a(ü— zl)4 + 2/?(zz — ü)2 + y
ac2— 4m = 0 scheidet aus.
V.
<P o /' — (Z2 + ü-^c)2 rf (c/Ö + ÖZ7) -j- (tzc) (ß 22-|-Ö 27 + 772) (7 (zz-|-D)
7? - — ~ I _ 3 '
• I ab(ii-\-ü-\-c)2— (ci v -j- b ii + m)2
(66) 2 (cz u + b u z/z)
Kcz b(/7 4" h c)2— (cz zJ-|-ö zz-j-77?)2
1
(C, + C, e-f<n+51)2 e ->+°> + <0~5>i d(a-D)
-3
+ 7
Be" - 2l9e4H"-|’>
(C1e_4(0_l’) —2m) (C, | 2‘" '''d(n | o)
- / -3
] / a e - ”1,1 - ” + 2 ß e ~2<“ -°> 4- r
Für aCy — 2mC2 =/=0 kommt durch Integration:
(67) F' ab(aCl2—2mC2j
C2e bü — 2aCr C2e~^u+Ü)- 2(ci Cy_—m CJ
y ae~b(n-D)^2ße--2{a-u)y-7
ciCy — 2mC2=0 scheidet aus.
0
vn.?f=j
('S [u (2 au2 — b z>4 2/c) — 2au‘i-\ 2bu2-\ 2(k —c)ü-\-d]dri
|z cc ll2 2 ß ll + y
/• 8 [ü (2 cz z72 4~ ö zz 4~ 2 /f) — 2 cz zz3 — 2 b ü 2 (/c — c) z7 — c/J du
>' |/’«z72 4-2^z7 4-73
89
15
IV.
Vcc(ü — ü)4 + 2 ^(z7 — ü)2 + 73
F=
F '
2(ü + y + c).[z??—-^(w —ü)2]rf(« + ü)
a (u — u)(u-\-u-y cY d(u — u)
]/a(zz— ü)4 + 2^(ü—n)2 + y3
Für cz c2 — 4 772 =y 0 ergibt sich:
0
(65) F t
2 !a(u— z?)2— 2 [2/72 — ac(2z + f + c)] z
a(ac2—4772) \ /a(ü— zl)4 + 2/?(zz — ü)2 + y
ac2— 4m = 0 scheidet aus.
V.
<P o /' — (Z2 + ü-^c)2 rf (c/Ö + ÖZ7) -j- (tzc) (ß 22-|-Ö 27 + 772) (7 (zz-|-D)
7? - — ~ I _ 3 '
• I ab(ii-\-ü-\-c)2— (ci v -j- b ii + m)2
(66) 2 (cz u + b u z/z)
Kcz b(/7 4" h c)2— (cz zJ-|-ö zz-j-77?)2
1
(C, + C, e-f<n+51)2 e ->+°> + <0~5>i d(a-D)
-3
+ 7
Be" - 2l9e4H"-|’>
(C1e_4(0_l’) —2m) (C, | 2‘" '''d(n | o)
- / -3
] / a e - ”1,1 - ” + 2 ß e ~2<“ -°> 4- r
Für aCy — 2mC2 =/=0 kommt durch Integration:
(67) F' ab(aCl2—2mC2j
C2e bü — 2aCr C2e~^u+Ü)- 2(ci Cy_—m CJ
y ae~b(n-D)^2ße--2{a-u)y-7
ciCy — 2mC2=0 scheidet aus.
0
vn.?f=j
('S [u (2 au2 — b z>4 2/c) — 2au‘i-\ 2bu2-\ 2(k —c)ü-\-d]dri
|z cc ll2 2 ß ll + y
/• 8 [ü (2 cz z72 4~ ö zz 4~ 2 /f) — 2 cz zz3 — 2 b ü 2 (/c — c) z7 — c/J du
>' |/’«z72 4-2^z7 4-73
89