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Построение линии пересечения 2-х конусов и цилиндра

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Ieienoa?noai iauaai e

i?ioanneiiaeueiiai ia?aciaaiey ?O

A?yineee Ainoaea?noaaiiue

Oaoie/aneee Oieaa?neoao

eaoaae?a

«Aunoay iaoaiaoeea»

?an/aoii-a?aoe/aneay ?aaioa ?1

Aa?eaio ?103

Nooaeaio a?oiiu 97AeII-1

Eiia/aa Ae.A.

I?aiiaeaaaoaeue

Naeeoia A.O.

A?yine 1997

1. Iienaiea ecaeaeey

Ia ?enoiea 1 ecia?aaeaii a o?ao i?iaeoeeyo ecaeaeea – iiaa?oiinoue,
ninoiyuay ec iaeiiai eonea oeeeeiae?e/aneie e aeaoo eoneia eiie/aneie
iiaa?oiinoae (EiEiOe).

Aeiiieieoaeueiua naaaeaiey:

?anoai? eiiona ( = 300

?aaeeon oeeeeiae?a R = 5 ni

?annoiyiea io ine eiiona aei ine oeeeeiae?a l =2 ni

?annoiyiea iaaeaeo inueth oeeeeiae?a e aa?oeiie eaaeaeiai ec eiionia L =
6 ni

Auai? nenoaiu eii?aeeiao

A ea/anoaa ia/aea eii?aeeiao aicueiai oi/eo ia?ana/aiey inae eiionia.
Inue aanoeenn ionoei aaeieue ine ia?aiai eiiona, inue i?aeeiao – aaeieue
ine aoi?iai eiiona, inue aiieeeao – ia?aeeaeueii ine oeeeeiae?a, i?e/ai
oae, /oiau nenoaia eii?aeeiao auea i?aaie.

?annoiyiea d io aa?oei eiionia aei ia/aea eii?aeeiao iaoiaeei n
iiiiuueth Oai?aiu Ieoaai?a:2

+ 2 = 7.7 (ni)

oaeei ia?acii inue oeeeeiae?a iienuaaaony neaaeothuei o?aaiaieai:

Aa?oeia ia?aiai eiiona eiaao neaaeothuea eii?aeeiaou – (-7.7; 0; 0),
aa?oeia aoi?iai eiiona – (0; -7.7; 0).

Aiaeeoe/aneia iienaiea ianoueo iiaa?oiinoae

O?aaiaiea oeeeeiae?e/aneie iiaa?oiinoe:

(o+2)2+(y+2)2 = R2 ( I )

Ia?aiao?ecaoeey oeeeeiae?e/aneie iiaa?oiinoe:

(II)

Ii?aaeaeaiea iieiaeaiey oaa ia oeeeeiae?e/aneie aeaoaee:

.

O?aaiaiea ia?aie eiie/aneie iiaa?oiinoe:

(x + 7.7)2 tg2( = y 2+ z2 (III)

Ia?aiao?ecaoeey ia?aie eiie/aneie iiaa?oiinoe:

(IV)

Ii?aaeaeaiea iieiaeaiey oaa ia ia?aie eiie/aneie aeaoaee:

iio?aaoai, /oiau (([-(sin(;(sin(]

Oiaaea oia aoaeao iaeaieaa oaeaeai io aoi?iai eiiona.

O?aaiaiea aoi?ie eiie/aneie iiaa?oiinoe:

(y+7.7)2 tg2(=x2+z2 (V)

Ia?aiao?ecaoeey aoi?ie eiie/aneie iiaa?oiinoe aiaeiae/ii ia?aie (IV):

(VI)

(Oaeaea iiaeii iaieoenue e aac iaa ca n/ao eniieueciaaiey neiiao?ee).

Iienaiea eeiee ia?ana/aiey oeeeeiae?a e ia?aiai eiiona ia aue?ieea
oeeeeiae?a

Iiaenoaaei ia?aiao?ecaoeeth oeeeeiae?a (II) a o?aaiaiea ia?aiai eiiona
(III), iieo/aai o?aaiaiea:

)2+v2, eioi?ia a aeaeueiaeoai i?aia?acoaony e aeaeo:

(VII)

Ciae «+» niioaaonoaoao «aa?oiae» iieiaeia eeiee io?aca, Z ( 0 , ciae «-»
– «ieaeiae» iieiaeia yoie eeiee. I?e iaeioi?uo cia/aieyo ia?aiao?a u
iiaeei?aiiia au?aaeaiea io?eoeaoaeueii, /oi niioaaonoaoao ionoonoaeth
ia?ana/aiey ia?acothuae oeeeeiae?a n ia?aui eiionii.

Iienaiea eeiee ia?ana/aiey oeeeeiae?a e aoi?iai eiiona ia aue?ieea
oeeeeiae?a

, iieo/aai eeieth ia?ana/aiey oeeeeiae?a ni aoi?ui eiionii.

Iienaiea eeiee ia?ana/aiey oeeeeiae?a e ia?aiai eiiona ia aue?ieea
eiiona

Iiaenoaaeyy ia?aiao?ecaoeeth ia?aiai eiiona (IV) a o?aaiaiea oeeeeiae?a
(I), iieo/aai o?aaiaiea:

+2)2 = R2

i?aia?acoai:

+2)2 = R2

+4-R2 = 0

)+36.49-R2 = 0

Ionthaea

(IX)

;

-5.7cos();

c=36.49-R2 .

Eeiey ia?ana/aiey neiiao?e/ia ioiineoaeueii eo/a (=0; aaoaue,
niioaaonoaothuay ciaeo «-» a oi?ioea (IX), iinoi?iiiyy.

Iienaiea eeiee ia?ana/aiey eiionia ia aue?ieea ia?aiai eiiona

Iiaenoaaeyy ia?aiao?ecaoeeth ia?aiai eiiona (IX), a o?aaiaiea aoi?iai
eiiona(V), iieo/aai o?aaiaiea:

eaaae?aoiia o?aaiaiea ioiineoaeueii ia?aiaiiie (.

Iinea oi?iuaiey iieo/ei:

tg2(+cos())+d2 (tg2(-1)=0

, (X)

;

tg2(+cos();

c = d2(tg2(-1).

Aue?ieea aoi?iai eiiona

Iia eaeaioe/ia aue?ieea ia?aiai eiiona.

?an/ao aue?ieee oeeeeiae?e/aneie aeaoaee

Iiaenoaaeyai a oi?ioeo (VII) eiie?aoiua /eneiaua aeaiiua e ?ann/eouaaai
ianeieueei oi/ae (u, v). ?acoeueoaou io/aoa caiinei a oaaeeoeo 1.

, iieo/aai eeieth ia?ana/aiey oeeeeiae?a ni aoi?ui eiionii. Iieoaunioo
oeeeeiae?a i?eiai ?aaiie 8 ni.

?an/ao aue?ieee eiie/aneeo aeaoaeae

I?iecaaaeai ?an/ao ii oi?ioeai ((; () ii oi?ioeai (IX, X). ?acoeueoaou
?an/aoia caiinei a oaaeeoeu 2 e 3.

?aaeeona (0=26ni., e, o/eouaay neiiao?e/iinoue ioiineoaeueii eo/a (=0,
iino?iei aue?ieeo eiie/aneie aeaoaee.

Ecaioiaeaiea aue?iae aeaoaeae, nai?ea ecaeaeey

Ecaioiaei aue?ieee aeaoaeae n i?eioneaie ia niaaeeiaiea eo a ecaeaeea,
o/eouaay i?aaeuaeouaa iienaiea. Au?aaeai e neeaei.

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