Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 26

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result obtained may also be evaluated. If we also compute
dy
— from (38a) or (43) and so are able to get approximate
values of the lowest derivatives of y with regard to
/, we can substitute for k_x (y) and /?, k_2 i^}\ in (37a)
\dt)
and (38a) their approximate values and thus gradually im-
prove our results,
Characteristic points of the curve may also be determi-
ned in this way, provided they are not too íar from the
origin (t — 0).
I shall here, as an example, consider a little closer the
dy o
case ,7 — 0 and determine t so that we have also u — 0.
rít a
The following equations give / with diminishing error as
we go to higher values of k.
From (37) or (40), k = 3:
at2 (1 -f e cos t) = 3 (46)
From (41), k — 3:
at2 (l-f e cos (í+ t)) = 2 (47)
From (37) or (45) for k—A:
5 at2 (1 -f e cosx) = 12 -f e af3sin x (48)
If t = 0, a = 4 and e = 0.6 we find from (46) the posi-
tive /= 0.685, from (48) t — 0.655 and from (37) for k —
5, t =0.620.
On the other hand from (41), for k = 3, (47), /=0.577,
for k = 4, / = 0,650, and for k = 5, / = 0.626. Hence we
conclude that the ríght value of / does not differ more
than 1 in the second decimal place from /=0.63. With
increasing k increasing accuracy in / is obtained. In simi-