Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 24

24
and
t _ n — o
dt ~
-* (- í)" d"ii
(k—n) [kn- at2( 1 + ecosT)]~— -----+
n! dt
k(k— 1) + ar(l + ecost)
(40)
We get another set ol solutions by using (25) and in this
case we confine ourselves to the first two terms or:
d2
t2 —2- + at2 (1 + e cos (t + T)) y (36a)
dt
I d3u du \
+ hií3 ~ ,3' + ö (1 + eCOS (t + t))— eay sin (f + x)j = 0
\ dt dt /
whence we get
-> 2 tn d"U
^(k-n)(k—l — n)[(k-l)(/c+2(n — 1)) — at (1 + Ecos(/+T))] -J'jf
/1= 0________;____ ________
D
(41)
D = k (k — l)2 (k — 2) + 2 (A’— 1) (fc - 3) ar (1 + e cos (t + T))
+ 2 (k — 1) eat3 sin (/ + T) + a'/4 (1 + e cos (/ + T))~
if
2 (k 1)
3 (k — 1) (k — 2) + at2 (1 +ecos (/+T))
(42)
dk~'y 0
whereby it fulfills the condition that ^ fc , disappears al-
so from the series in (41).
Likewise we obtain from (36a):