Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 26

Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 26
26 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-

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Rit (Vísindafélag Íslendinga)

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