Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 25

25
-> tn d"ij0
dy _ ^r0_ __ n\ dt
dt D
(43)
P = nk {k — 1) — {2k — 4 + n) at2 {1 + e cos {t + T)) — eat3sin {t + t)
D = k {k - l)2 {k - 2) + 2 {k — 1) {k - 3) (1 + e cos {t +1)) at2
+ 2 {l( — 1) e at3 sin {t +1) + a2 f' (1 + e cos {t +1))“
if
at2 (1 + e cos {t +1)) k{k 1) (42a)
4i =
2 k {k — 1) {k — 2) + e at sin {t + t)
Further, corresponding formulas for the other end of the in-
terval:
—>
\ (k — n){k— 1 — n) [(/c — 2 + 2u) {k — 1) — ar(l +eCost)]
y n ■—
n= 0
{-t)n dny
n\ din
= k [k — l)2 {k — 2) + 2 {k — 1) {k — 3) at2 (1 + e cos t)
— 2{k— 1) eaí3sint + aV(l + ecost)2
(— t)" d"y
(K—n)(K—i— ri)
i o
(44)
■t
^Tik-n^ik-l-n^P,
dy0 ri\ dt
dt
D,
(45)
Pj — nk(k— 1) — (2k — 4 + n) at1 (1 + e cost) + e aí3sin t
+/o
If y0 and are known, the formulas (37) or (37a) and
dt
(41) enable us to calculate y and we need not go to large
values of k provided that t is small. The accuracy of the