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Cell[CellGroupData[{
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 "Ujuja trajektoor 90",
 "\[Degree]",
 " ",
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 "hoovuse puhul, kui suunda hoitakse teatud punktile."
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Cell["Eelmise mudeli vigadest", "Subsubsection",
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Cell[TextData[{
 "Eelmisel mudelil, mis ei kasutanud diferentsiaalv\[OTilde]rrandite \
lahendamisv\[OTilde]tteid, ilmnesid olulised puudused.\nNagu \
m\[ADoubleDot]rkis Rando, ei saa siis, kui ujuja omakiirus ",
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 "ja j\[OTilde]e voolu kiirus ",
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 " on v\[OTilde]rdsed, mitte mingil juhul vastuvoolu liikuda (isegi mingil v\
\[ADoubleDot]ikesel osal trajektoorist!); ka on vastuvoolu liikumine v\
\[OTilde]imatu loomulikult juhul, kui ujuja kiirus on v\[ADoubleDot]iksem j\
\[OTilde]e voolu kiirusest. Olgu  ",
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 "Kui ",
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 " >1, siis on ujuja kiirus seisvas vees  suurem j\[OTilde]e voolamise \
kiirusest; kui ",
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 "= 1, siis on need kiirused v\[OTilde]rdsed; kui ",
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 "<1, siis voolab j\[OTilde]gi ujujast kiiremini. "
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Cell[TextData[{
 "Allj\[ADoubleDot]rgnevatel joonistel on kujutatud trajektoore erinevate k v\
\[ADoubleDot]\[ADoubleDot]rtuste korral. Paraku on arvuti poolt \
v\[ADoubleDot]lja joonistatud trajektooride hulgas ka selliseid (",
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 " = 0, 98, ",
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 " = 0.95, mille puhul toimus \[UDoubleDot]lalmainitud kiiruste puhul \
vastuvoolu liikumine. "
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Esimese mudeli puhul sai v\[ADoubleDot]lditud diferentsiaalv\[OTilde]rrandite \
kasutamist. Teise mudeli puhul said matemaatiliseks aparatuuriks aga just \
nimelt diferentsiaalv\[OTilde]rrandid. 
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Teine mudel leiab trajektooride v\[OTilde]rrandid \
diferentsiaalv\[OTilde]rrandite anal\[UDoubleDot]\[UDoubleDot]tilise \
lahendamise 
teel ja selle algallikas paikneb aadressil:

 https://answers.yahoo.com/question/index?qid=20081023044325AAVQb0z

T\[OTilde]lkisin selle lahenduse eesti keelde, lisasin veidike kommentaare, 
muutsin kohati t\[ADoubleDot]histusviisi m\[OTilde]istlikumaks ja \
k\[OTilde]rvaldasin \[UDoubleDot]he pisivea. 
Minu tegevuse tulemuse v\[OTilde]ib leida aadressilt

 http://www.tlu.ee/~tonu/modesimu/difvorrandid/ujujatrajektoor2.pdf
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f\[UDoubleDot]\[UDoubleDot]sikaliselt usaldusv\[ADoubleDot]\[ADoubleDot]rsem \
kui eelmine mudel, mis ei kasutanud diferentsiaalv\[OTilde]rrandite s\
\[UDoubleDot]steemi \nanal\[UDoubleDot]\[UDoubleDot]tilist lahendamist, vaid \
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Samas, tegin \[ADoubleDot]ra esimesed katsed selliste liikumise \
diferentsiaalv\[OTilde]rranditega, mille puhul ujujale v\[OTilde]i 
kajakimatkajale m\[OTilde]jub m\[OTilde]jub hoovus 90 kraadisest nurgast \
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hetkel neid v\[OTilde]rrandeid lollikindlal meetodil lahendada ei \
m\[OTilde]ista, siis proovisin numbrilist lahendamist 
ja \[UDoubleDot]llatav k\[UDoubleDot]ll, sain juba v\[ADoubleDot]ga h\
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90 
kraadise erijuhtumi puhul langevad kokku antud mudeli omadega. Lisaks muule \
paistab, et numbriliste 
meetodite puhul ei ole raske m\[ADoubleDot]\[ADoubleDot]rata ka trajektoori l\
\[ADoubleDot]bimiseks kuluvat aega.
 
01.05.2014. T\[OTilde]nu T\[OTilde]nso
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