Proyecto Final Cinematica y Dinamica de Maquinas

 

XIB^HU[BAJA AH MXJAJDJLJUJ KHIQUF XIB^HU[BQJUBF AH KBHIKBJ[ HSJKQJ[ H BIMHIBHUÏJ[ AB^B[BÛI AH BIMHIBHUÏJ[

WUFRHKQF7377 377 ?3;.==rja = rjashm

Rj kfi dfs ajtfs hi djs uibajahs kfrrhktjs sh pfarê bibkbjr kfi hd jiêdbsbs<

5.:. ^hdfkbajahs Ajaf dfs ajtfs quh sh kfifkhi kfif khi ahd ohkjibsof, hs ahkbr dj kfopfs kfopfsbkbûi bkbûi y dfkjdbzjkbûi ah dfs hsdjefihs y pjrhs kbihoêtbkfs hi hd ohkjibsof sh puhahi bahitbnbkjr djs bikûmibtjs ahd sbsthoj, abkcjs bikûmibtjs sh hikuhitrji hi hd puitf K; ah rftjkbûi y K; ah trjsdjkbûi, yj quh sh ahskfifkh dj vhdfkbaja jimudjr ahd hsdjeûi ;, hs ahkbr su ojmibtua, abrhkkbûi y shitbaf. Abkcf hstf, kfi hd jiêdbsbs jithrbfr, sh puhah prfkhahr j cjkhr dfs rhsphktbvfs kêdkudfs kfi  ejsh j ahskfopfsbkbûi ah djs hhkujkbfihs kujkbfihs ah vhdfkbaja ahd ohkjibsof, o hkjibsof, hophzjiaf kfi djs bikûmibtjs quh yj sh kfifkhi, kfistruyhiaf dj hkujkbûi (5)<

v⃝t ? v⃝ t

 

(5)

Duhmf ah hsth pjsf, sh ahsmdfsjrê kjaj hxtrhof ah hstj bmujdaja ah ojihrj biabvbaujd hophzjiaf kfi

v⃝t

 sh bmujdjrê j dj vhdfkbaja ahd puitf jithrbfr quh hs E;  y j dj vhdfkbaja

rhdjtbvj K;E; fethibhiaf jsï dj hkujkbûi (;)<

 

 

v⃝t ? v⃝  + v⃝ 

(;)

 

Df uiïkf quh sh kfifkh ah dj vhdfkbaja rhdjtbvj K;E; hs su abrhkkbûi, yj quh jd hstjr hi ui  pjr kbihoêtbkf ah rftjkbûi ahehrê hstjr phrphiabkudjr phrphiabk udjr j dj dfimbtua EK. [bmubhiaf kfi hd ahsmdfsh, dj vhdfkbaja   E;  sh bmujdj kfi dj vhdfkbaja   E5  ahebaf j quh hd hsdjeûi 5 y ; kfinfroji hd pjr kbihoêtbkf E nfroudjiaf ah hstj ojihrj dj  hkujkbûi (1))<

v⃝  ? v⃝ 

 

Rj kfi hd ahsmdfsh kfopdhtf ahd hxtrhof bzqubhraf (

(>)

v⃝t

ah iuhstrj hkujkbûi  (5) sh 

 prfkhahrê jcfrj j ahskfopfihr hd hxtrhof ahrhkcf ah hstj obsoj hkujkbûi  sbmubhith ojihrj<

K;K1

v⃝t

  ah dj 

  y j dj rhdjtbvj ah hstjs afs, dj vhdfkbaja

[h bmujdjrê j su puitf jithrbfr dj vhdfkbaja  fethibhiaf jsï dj  hkujkbûi (=)<

 

^K1

 

v⃝ t ? v⃝  + v⃝ 

Df uiïkf quh sh kfifkh ah dj hkujkbûi (=)  hs quh dj vhdfkbaja rhdjtbvj  dfimbtua EK, ahebaf j quh phrthihkh j ui pjr ah trjsdjkbûi.   Ahspuâs ah hstf, sh ahehrê shpjrjr j dj vhdfkbaja

(=)

 

K;K1

 hs pjrjdhdj j dj

 y sh bmujdjrê j dj vhdfkbaja

K1

 pfrquh

^K:

hd hsdjeûi : y 1 kfinfroji hd pjr kbihoêtbkf K, kfi hstj bmujdjkbûi sh puhah hdbobijr dj vhdfkbaja

K:

 ahebaf j quh hd hsdjeûi : hs uij ejsh, pfr df quh su vhdfkbaja hs 7, abkcf puitf

jd hstjr bmujdjaf kfi dj vhdfkbaja jsï dj hkujkbûi (3)<

K1

 cjkh quh hstj üdtboj tjoebâi sh hdbobih, kfinfrojiaf

v⃝  ? v⃝ 

  (3)

5.:.:. Uhsfdukbfi ah djs hkujkbfihs ah vhdfkbajahs

v⃝t ? v⃝ t v⃝ t  v⃝ + v⃝  ⃝v ? v⃝  ⃝v ? v⃝  + v⃝  rja ? ⃝v v ⃝ o   v⃝  ? 3;.== s  : o ?3;.== s   ⃝vt ? ⃝v + ⃝v ⃝v ? ⃝v  

?

 

 

 

 

 

 

Hd cjehr ahskfopuhstf djs vhdfkbajahs ah iuhstrf ohkjibsof sbrvbû pjrj sjehr quâ ojmibtuahs sh pfaïji kjdkudjr kfi dfs ajtfs quh sh tbhihi y quâ ftrfs ajtfs sh thiarêi quh

 

 

kjdkudjr kfi hd oâtfaf ahd pfdïmfif kfi ejsh j djs kjrêkthrïstbkjs ah hstjs vhdfkbajahs, hs pfr hddf quh sh luitjrêi tfafs dfs ajtfs kfifkbafs hi uij hkujkbûi quh shrvbrê pjrj trjzjr hd  pfdïmfif ah vhdfkbajahs quh sh ifoerjrê kfof dj  hkujkbûi (2)<

 

(2)

v⃝ + v⃝  ? v⃝ E5J5+ v⃝ 

Jiths ah trjzjr hd pfdïmfif ah vhdfkbajahs hs ihkhsjrbf hstjedhkhr uij hskjdj pjrj hd abeulf, hstf sh cjkh abvbabhiaf iuhstrj vhdfkbaja rhdjtbvj   hsth kjsf ;7 oo<

  hitrh uij ohabaj ah dfimbtua, hi

o 3;. = = ¸ ? ;7 oos ?5.=25 os /oo

Kfi dj hskjdj yj hstjedhkbaj y kfi dj hkujkbûi (2) sh prfkhah j trjzjr hd pfdïmfif (Nbmurj 3)<

Nbmurj 3. Wfdïmfif ah vhdfkbajahs ahd ohkjibsof Rj trjzjaf hd pfdïmfif sh puhahi kjdkudjr djs vhdfkbajahs rhdjtbvjs njdtjiths (

K;E; y K;K1

obabhiaf dj dfimbtua ah hstjs y oudtbpdbkjiafdjs kfi dj hskjdj ah vhdfkbajahs prhvbjohith hstjedhkbaj<

o 5. = 25 v⃝  ? :3 oo oo  oo s  ?87.5> os

 

 

 

o 5. = 25 v⃝  ? 58 oo oo  oo s  ?>2.3 os

 

Wfr üdtbof sh kjdkudj df quh sh hstjej euskjiaf hi ui prbikbpbf, dj vhdfkbaja jimudjr ;, abvbabhiaf dj vhdfkbaja rhdjtbvj

 hitrh dj dfimbtua EK<

K;K1 ς ? 87.5.35>o>oos ?:=.28 os

 

Kfi dj jyuaj ahd pfdïmfif ah vhdfkbajahs prhvbjohith trjzjaf tjoebâi sh puhah sjehr dj abrhkkbûi y shitbaf ah

ς

, pfr df quh j kfitbiujkbûi sh ofstrjrê hd abjmrjoj abjmrjo j ahd ohkjibsof

kfi kjaj uij ah sus vhdfkbajahs hi sus abrhkkbfihs y shitbafs kfrrhspfiabhiths kfof vhofs hi dj nbmurj 2<

Nbmurj 2. Uhprhshitjkbûi ah dfs vhktfrhs ah vhdfkbaja hi hd ohkjibsof

5.5. Jkhdhrjkbfihs Wjrj djs jkhdhrjkbfihs sh cjkh ui prfkhabobhitf sbobdjr jd ah djs vhdfkbajahs, sjebhiaf quh djs bikûmibtjs sh hikuhitrji hi hd puitf K; ah rftjkbûi y K; ah trjsdjkbûi y sh rhqubhrh sjehr dj ojmibtua, dj abrhkkbfi y hd shitbaf ah dj jkhdhrjkbfi jimudjr ; sh pdjithj dj sbmubhith hkujkbfi<

  t t   j⃝ ? j⃝

(:7)

 

 

Ahspuhs sh ahsmdfsji djs jkhdhrjkbfihs ah dj hkujkbfi (:7), hophzjiaf kfi

j⃝t

 hi afiah

hstj sh bmujdj j dj jkhdhrjkbfi ah su puitf jithrbfr quh hs E;, j dj rhdjtbvj ifrojd K;E; y j dj rhdjtbvj tjimhikbjd K;E;, quhajiaf ah dj sbmubhith nfroj<

t  t j⃝  ? j⃝  + j⃝  + j⃝  j⃝  ? ςD 

 

(::)

Ah dj hkujkbfi (:7) sh puhah kfifkhr dj ojmibtua ah dj jkhdhrjkbfi rhdjtbvj ifrojd K;E; kfi dj nfroudj abrhktj<

Whrf ah dj hkujkbfi (::) sh ahskfifkh dj ojmibtua ah dj jkhdhrjkbfi rhdjtbvj tjimhikbjd ah K;E; phrf jd hstjr hi ui pjr kbihojtbkf ah rftjkbfi kfifkhofs su abrhkkbfi quh hs  phrphiabkudjr j EK. [bmubhiaf kfi hd ahsmdfsh ah djs jkhdhrjkbfihs, sh tbhih quh ddjj jkhdhrjkbfi ah E; hs bmujd dj jkhdhrjkbfi ah E5 ahebaf j quh dfs hsdjefihs 5 y ; kfinfroji hd pjr kbihojtbkf E nfroudjiaf ah hstj ojihrj dj hkujkbfi (:5)<

j⃝  ? j⃝ 

(:5)

 

Jcfrj dj jkhdhrjkbfi E5 sh ahsmdfsj kfi dj jkhdhrjkbfi ahd puitf jithrbfr j hstj quh hs dj jkhdhrjkbfi J5, dj jkhdhrjkbfi rhdjtbvj ifrojd E5J5 y dj jkhdhrjkbfi rhdjtbvj tjimhikbjd E5J5, kfinfrojiaf jsb dj hkujkbfi (:;)<

 

(:;)

j⃝ ? j⃝  + j⃝  + j⃝ t j⃝  ? ςD

Jd kfitjr kfi dj nfroudj abrhktj pjrj kjdkudjr dj ojmibtua ah djs jkhdhrjkbfihs ifrojdhs tjoebhi sh puhah kfifkhr dj jkhdhrjkbfi rhdjtbvj ifrojd E5J5 ah dj sbmubhith nfroj<

 

Qjoebhi sh sjeh quh jd thihr uij vhdfkbaja jimudjr kfistjith hi hd hsdjefi 5, if sh puhah thihr uij jkhdhrjkbfi jimudjr 5 y pfr dj nfroudj abrhktj pjrj kjdkudjr dj ojmibtua ah djs jkhdhrjkbfihs tjimhikbjdhs, dj jkhdhrjkbfi rhdjtbvj tjimhikbjd E5J5 hs khrf.

 

 

Wfsthrbfrohith, sh bmujdj dj jkhdhrjkbfi J5 kfi dj jkhdhrjkbfi ah su puitf jithrbfr quh hs J:, hi afiah hd hsdjefi : y 5 kfinfroji hd pjr kbihojtkf J quh sh hikuhitrj hi dj ejsh y  pfr hstj rjzfi djs jkhdhrjkbfihs sfi khrf, nfrojiaf dj hkujkbfi (:1)< (:1) < (:1)

 

j⃝ ? j⃝ 

Rj kfi hd ahsmdfsh kfopdhtf ah dj jkhdhrjkbfi K; ah rftjkbfi sh prfkhahrê j cjkhr dj ahskfopfsbkbûi ah dj jkhdhrjkbûi K; ah trjsdjkbûi ah dj sbmubhith ojihrj< [h bmujdjrê hd puitf jithrbfr, hi hsth kjsf dj jkhdhrjkbûi K1 y sh ahskfopfiarê djs jkhdhrjkbfihs hi sus kfopfihiths kfrbfdbs (pfr shr ui pjr ah trjsdjkbûi) y tjimhikbjd fethibhiaf dj hkujkbûi (:8)<

j⃝t ? j⃝  + j⃝  + j⃝ t

 

(:8)

Ah dj hkujkbûi (:1) sh puhah kjdkudjr y sjehr dj ojmibtua, abrhkkbûi y shitbaf ah dj jkhdhrjkbûi kfrbfdbs K;K1, dj ojmibtua sh kjdkudj oudtbpdbkjiaf 5 pfr dj vhdfkbaja jimudjr ; y dj vhdfkbaja K;K1, su abrhkkbûi y shitbaf sh puhah sjehr rftjiaf ah ojihrj phrphiabkudjr dj vhdfkbaja K;K1 kfi ejsh j dj abrhkkbûi y shitbaf ah dj vhdfkbaja jimudjr ;, hstf ahebaf j quh hs dj jkhdhrjkbûi quh hxphrbohitj dj kfrrhahrj ahebaf jd mbrf ahd hsdjeûi ;.

j⃝ ? ς5v⃝ 

 

Qjoebâi ah hstj hkujkbûi sh kfifkh dj abrhkkbûi ah dj jkhdhrjkbûi tjimhikbjd K;K1 quh hs  pjrjdhdf j dj dfimbtua EK ahebaf j quh hs ui pjr kbihoêtbkf ah trjsdjkbûi. Wfr üdtbof dj jkhdhrjkbûi K1 sh shpjrj y sh bmujdj j dj jkhdhrjkbûi K: yj quh dfs hsdjefihs : y 1 kfinfroji hd pjr kbihoêtbkf K, hd hsdjeûi : jd shr uij ejsh su jkhdhrjkbûi hs bmujd j 7, kfi hstf sh puhah hdbobijr dj jkhdhrjkbûi K1 nfroudjiaf jsï dj hkujkbûi (:>)<

j⃝  ? j⃝ 

  (:>)

 

 

5.5.:. Uhsfdukbfi ah djs hkujkbfihs ah jkhdhrjkbfihs

j⃝t ? j⃝ t j⃝ t ? j⃝ j⃝ +?j⃝ j⃝  + j⃝ t j⃝  ? j⃝  + j⃝  + j⃝ t j⃝  ? j⃝   

 

 

 

 

j⃝  ? 3;.== rjas  : oo ?=7:=.1: os     j⃝  ? 51.255rja  rjas 5.3 oo ?:=17.5:o: os

j⃝t ? j⃝  + j⃝  + j⃝ t j⃝  ? j⃝ 

 

 

j⃝ ?51.25   5 >2.3   ? ;1=3.3; 

 

Hd cjehr ahskfopuhstf djs jkhdhrjkbfihs ah iuhstrf ohkjibsof sbrvbû pjrj sjehr quâ ojmibtuahs sh pfaïji kjdkudjr kfi dfs ajtfs quh sh tbhihi y quâ ftrfs ajtfs sh thiarêi quh kjdkudjr kfi hd oâtfaf ahd pfdïmfif kfi ejsh j djs kjrêkthrïstbkjs ah hstjs jkhdhrjkbfihs, hs  pfr hddf quh sh luitjrêi tfafs dfs ajtfs kfifkbafs hi uij hkujkbûi quh shrvbrê pjrj trjzjr hd  pfdïmfif ah vhdfkbajahs quh sh ifoerjrê kfof dj hkujkbûi (:=)<

j⃝  + j⃝  + j⃝ t ? j⃝  + j⃝  + j⃝ t

 

(:=)

Jiths ah trjzjr hd pfdïmfif ah jkhdhrjkbfihs hs ihkhsjrbf hstjedhkhr uij hskjdj hskj dj pjrj hd abeulf, hi hsth kjsf sh kfifkhi ; jkhdhrjkbfihs, dj jkhdhrjkbûi ifrojd K;E;, dj jkhdhrjkbûi ifrojd E5J5 y dj jkhdhrjkbûi kfrbfdbs K;K1, hs ihkhsjrbf sjkjr djs hskjdjs ah hstjs ; jkhdhrjkbfihs,

 

 prbohrf sh abvbabrê dj ojmibtua ah dj jkhdhrjkbûi E5J5 hitrh dj ojmibtua ah ;7 oo, hd kfkbhith ah hstj fphrjkbûi shrvbrê pjrj kjdkudjr hd vjdfr hi oo ah dfs vhktfrhs ah dfs ftrfs vhktfrhs ah jkhdhrjkbûi kuyjs ojmibtuahs sh kfifkhi, abvbabhiaf abkcjs ojmibtuahs hitrh hd vjdfr ah dj hskjdj prhvbjohith kjdkudjaf ah dj sbmubhith ojihrj<

¸ ? =7:=.;7 oo1:o: o ?5;;. 2:o: o /oo k;∝e;∝ ? ../  .    ∝ ∝ k; k1 ? ./

 

? =.1; oo

? :1.3= oo

Kfi dj hskjdj yj hstjedhkbaj y kfi dj hkujkbûi (:=) sh prfkhah j trjzjr hd pfdïmfif (Nbmurj :7)<

Nbmurj :7. Wfdïmfif ah jkhdhrjkbfihs ahd ohkjibsof Rj trjzjaf hd pfdïmfif sh puhahi kjdkudjr djs jkhdhrjkbfihs tjimhikbjdhs njdtjiths (K;E; y K;K1) y dj jkhdhrjkbfi rhsudtjith K;K1 obabhiaf dj dfimbtua ah hstjs y oudtbpdbkjiafdjs kfi dj hskjdj ah jkhdhrjkbfihs prhvbjohith hstjedhkbaj<

5;;.2: o j⃝ t ? 17 oo oo  oo s  ?2;8>.1 so 

 

o 5;;. 2 : j⃝ t ? 3 oo oo  oo s ?:3=:.53 so 5;;.2: o o j⃝  ? :> oo oo  oo s  ?;=15.8> s o   :3=:. 5 3  s κ ? 5.3 o ?>>3.;: rjas

 

 

Wfr üdtbof sh kjdkudj df quh sh hstjej euskjiaf, dj jkhdhrjkbûi jimudjr ;, abvbabhiaf dj jkhdhrjkbûi tjimhikbjd K;K1 hitrh dj dfimbtua EK<

 

Kfi dj jyuaj ahd pfdïmfif ah jkhdhrjkbfihs prhvbjohith trjzjaf tjoebâi sh puhah sjehr dj abrhkkbûi y shitbaf ah κ;, pfr df quh j kfitbiujkbûi sh ofstrjrê hd abjmrjoj ahd ohkjibsof kfi kjaj uij ah sus jkhdhrjkbfihs hi sus abrhkkbfihs abrh kkbfihs y shitbafs kfrrhspfiabhiths ((Nbmurj Nbmurj ::)<

Nbmurj ::. Uhprhshitjkbûi ah dfs vhktfrhs ah hi hd ohkjibsof

 

;. Jiêdbsbs Abiêobkf Bibkbjiaf kfi hd kêdkudf ah nuhrzjs ahd ohkjibsof (Nbmurj ;), prbohrjohith hs ihkhsjrbf kfifkhr dfs ajtfs prbikbpjdhs prbohrjohith hxprhsjafs ah ojihrj mhihrjd (o y L) ahspuhs  prfkhahr j su ahsjrrfddf kfi dfs ajtfs ohikbfijafs o hikbfijafs hi dj (Nbmurj 5), 5 ), jd bmujd quh dfs ajtfs fethibafs hi hd ofaudf jithrbfr. Ajtfs mhihrjdhs<

o?3D

L ? 7.7:= oD

 

 

Jd fethihr dfs ajtfs mhihrjdhs sh puhah kfitbiujr kfi dfs kjdkudfs phrtbihiths, phrtbihiths , ah hstj ojihrj sh kfifkhi djs ojsjs ah kjaj uif ah dfs hsdjefihs tjitf ah dj ojiïvhdj kfof ah dj ebhdj, jahoês ah hstf sh kjdkudjrê dj vjrbjedh —L‟ quh shrê ihkhsjrbj ojs jahdjith.        d   d  o ? 3  ? 5. 3  o o :  o o ?  ? 55. 55 3 . 1 @ @m m Ld ?7.7:=55.1 @m5.3 o ? 5.2381 @m ∝ o  Ld ?7.7:=3 @m: o ? 7.:;> @m ∝ o  Chkcf hstf tfafs dfs ajtfs mhihrjdhs sh vuhdvhi tftjdohith kfifkbafs ah tjd ojihrj quh sh puhahi ahnbibr luitf kfi dfs ajtfs quh fetuvbofs hi hd ofaudf pjsjaf. Ajtfs kfifkbafs<

od ? 55.55.1 @m od ? 3 @m j ?2;8>.1 so κ ?>>3.;: rjas

   

 

 

Ld ? 5.2381 @m ∝ o Ld ? 7.:;> @m ∝ o N ? :=>7 :=>7 I j ?=7:=.1: so  

 

 

 

 

Kfof prbohr pjsf sh bibkbjrê ahnbibhiaf tfajs djs bikfmibtjs hi hd ohkjibsof jiths  pdjithjaf pjrj cjkhr ui u i jiêdbsbs oês ahtjddjaf h bahitbnbkjr tjitf ojmibtua kfof sshitbaf hitbaf ah kjaj uij ah djs nuhrzjs kfof sh ouhstrj hi dj nbmurj :5<

Nbmurj :5. Bikfmibtjs ah Nuhrzjs Kfof shmuiaf pjsf sh ahnbihi tfajs djs nuhrzjs y ofohitfs bihrkbjdhs quh sh ahthrobijrfi hi dj (Nbmurj :5) jahoês ah djs ojsjs ah dfs hsdjefihs hi kuhstbûi.

 ?∕ ∕;;.1 2;8 2;8>.>.1   ? ∕;;.  ? ∕   ? 7

 

?57283;.;> I

(

 

 

Kfof sh feshrvj hi djs nfroudjs jithrbfrhs kjdkudû djs nuhrzjs bihrkbjdhs ah joefs hsdjefihs uiïkjohith oudtbpdbkjiaf dj ojsj pfr dj jkhdhrjkbfi, ah hstj ojihrj sh kfifkhrêi hstjs bikfmibtjs quh utbdbzjrhofs hi dfs kêdkudfs oês jahdjith. Kjeh shújdjr quh

N

 sh kfivbhrth

hi khrf yj quh dj ojsj ah abkcf hsdjeûi hs ahsprhkbjedh f oïiboj pfr df quh jd rhjdbzjr djs fphrjkbfihs phrtbihiths feshrvjofs quh su ojmibtua hs khrf. Ah bmujd ojihrj sh ahsjrrfddji dfs ofohitfs bihrkbjdhs prbohrjohith kfi hkujkbfihs mhihrjdhs pjrj pfsthrbfrohith kfi dfs vjdfrhs iüohrbkfs phrtbihiths, hstfs ajtfs luitf kfi kjaj uif ah dfs jithrbfrhs shrêi utbdbzjafs oês jahdjith ja hdjith hi djs suojtfrbjs tjitf ah ofohitfs kfof ah nuhrzjs.

 

 

O ? ∕Lκ O ? ∕5.22381381 @m∝@m ∝ o >>3.;: rjas  ? :228.55 I ∝ o  

Wfr ftrf djaf

O ? 7

 

    O?∕ ? 7  

 ahebaf j quh hi hd hsdjeûi 1 (Nbmurj ;) if hxbsth uij jkhdhrjkbûi, hs

ahkbr quh hstj hs khrf, pfr hiah dj oudtbpdbkjkbûi ahd obsof hs khrf df kujd sbmibnbkj quh hsh ofohitf if hs tfojaf hi kuhitj hi hd kêdkudf. Wjrj nbijdbzjr hd kêdkudf ah tfajs djs bikfmibtjs bibkbjdhs sh prfkhah j fethihr djs ojsjs ah kjaj hsdjeûi jsï kfof dj ojsj ahd hsdjefi 5 (Nbmurj ;) pjrj kfohizjr kfi hd ahsjrrfddf oês ahtjddjaf ahd sbsthoj.

] ? omm  ] ? omm  ] ? 55.1 @m 2.3: so ? 5:2.=1 I  ] ? 3 @m 2.3: so ? =3.13 I Hi hsth kjsf ]  hs hs khrf yj quh dj ojsj ahd hsdjeûi 1 (Nbmurj ;) hs ahsprhkbjedh y tfojofs kfof vjdfr khrf y jd rhjdbzjr djs fphrjkbfihs sh fetbhih abkcf vjdfr.

Hd jijdbsbs ah nuhrzjs kfistj ah 1 pjsfs prbikbpjdhs dfs kuêdhs tbhihi kfof ejsh dj suojtfrbj ah nuhrzjs f ah ofohitfs shmüi shj hd kjsf. Hd ohkjibsof j jijdbzjr kfisbsth hi ui ohkjibsof ah shmuiaj kdjsh shmuiaj vjrbhaja pfr df quh hd prbohr pjsf hs uij suoj ah ofohitfs hi hd hsdjefi ;. Kfi dj nbijdbaja ah kfifkhr uij ah iuhstrjs bikfmibtjs dj kuêd hs

Nt :. Ϋ O; ? 7

dj

, hstf sh ouhstrj hi dj hkujkbûi (:3)<

[ustbtukbûi<

 

(Nt ∝ D)∕(O) + w ∝ c ∝ ¸ + (N ∝ c ∝ ¸) ? 7

 

(:3)

 

∕Nt ∝ 5.3 o ∕ :2:22828..55 I ∝ o +5:2.=1 I∝=7 oo∝7.75 ooo  + 5572728383;.;.;> I∝I ∝ >7 oooo ∝ 7.75 ooo  ? 7  

Xij vhz ahnbibaj dj suojtfrbj ah ofohitfs y sustbtuyhiaf dfs vjdfrhs kfifkbafs, kfifkbafs, quhajrê uij suoj ah ofohitfs kfi uij bikfmibtj, pjrj rhsfdvhr hstj suojtfrbj sh ahsphlj pjrj

 

fethibhiaf fethibhiaf dj ojmibtua y dj abrhkkbfi ah iuhstrj prbohr nuhrzj<

∕325:3.:3.=;=;  ∕Nt ? :228.55 I∝I ∝ o ∕ ;7=.>;5.>3I∝Io∝ o ∕ 58:872.7;> II∝∝ o ? ∕325 Nt ? 325: 325:3.3.=; 

 

 

Hs bopfrtjith rhkfrajr quh hd sbmif ohifs sbopdhohith hs ui biabkjafr ah pfsbkbûi df quh  phrobth vbsujdbzjr su shitbaf ah ojihrj kfrrhktj quh pjrj hnhktfs ah kêdkudfs k êdkudfs hsth sh fobth. Kfof sbmubhith pjsf sh prfkhah cjkhr uij suojtfrbj (hkujkbûi (:2)) ah nuhrzjs hi joefs hsdjefihs hs ahkbr djs nuhrzjs quh jktuji sferh hd hsdjeûi ; y sferh hd hsdjeûi 1 kfi dj

N N 5. Ϋ N;, 1 ? 7 N + (Nt) + w + (N) + N + N ? 7 nbijdbaja ah kfifkhr afs ah djs bikfmibtjs djs kujdhs sfi <

 y

 

 

 

(:2)

[ustbtuyhiaf vjdfrhs hi dj hkujkbûi (:2) thihofs<   N + 325:3   25 :3. . = ; I I+ + 5: 5:2. 2. = 1 I I+ + 57 5728 283; 3;. . ; > I I+ + :=>7 := >7 I + N ? 7 Kfof sh feshrvj hi dj hkujkbfi jithrbfr thihofs afs bikfmibtjs ah djs kujdhs kfifkhofs   hs pjrjdhdj j EK y sh kfifkh tjoebhi quh  hs phrphiabkudjr j EK ah bmujd ojihrj, quh N

 pfr hstj fk fkjsbûi jsbûi sh trjzjrê ui pfdïmfif vhktfrbjd pjrj quh ah hstj ojihrj o jihrj ahthrobijr tjitf ojmibtua kfof shitbaf ah joejs nuhrzjs. Wjrj hddf sh prfkhah prbohrf j kjdkudjr uij hskjdj ah nuhrzjs dj kujd hs dj sbmubhith<

325:3.=; I I ¸ ? ;7 oo ?52=;.28 oo

 

 

Xij vhz kjdkudjaj dj hskjdj ah nuhrzjs, sh ahthrobij dj dfimbtua ah kjaj uij ah djs nuhrzjs yj kfifkbajs, abvbabhiaf su ojmibtua hitrh dj hskjdj ah nuhrzjs fethibaj pjrj quh ah hstj ojihrj sh puhaj trjzjr hd pfdbmfif ah nuhrzjs.

5:2.=1 I wn  ?? 57283;. 52=;.28;oooo?7. >III ?7.?27.7=;1= oooo 52=;.28 oo n  ? 52=;.:=>728IooI ? 7.82:32:3 oooo  

 

 

Xij vhz fethibajs djs hskjdjs ah djs nuhrzjs nu hrzjs sh prfkhah j abeuljr hd pfdïmfif ah nuhrzjs kfof sh vh hi dj nbmurj :;<

Nbmurj :;. Wfdbmfif ah Nuhrzjs Ahd pfdïmfif ah nuhrzjs sh sjkjrê dj ohabaj hi obdïohtrfs ah djs afs bikfmibtjs, jsb obsof ahspuâs sh prfkhah j oudtbpdbkjr abkcf vjdfr pfr dj hskjdj ah jkhdhrjkbfihs pjrj fethihr dj ojmibtua ah djs nuhrzjs.

52=;..28 I ?:5;82=.;> I N ? 1:.1:.8> oooo∝∝ 52=; oo

 

 

N ? 7 oooo ∝ 52=;.28 ooI ? 7 I

 

Kfof thrkhr pjsf sh tbhih uij suojtfrbj suojtfr bj (hkujkbûi 57) ah nuhrzjs hi hd hsdjeûi 1, obsoj quh  phrobtbrê kfifkhr dj ;.

(

Ϋ N 1?7

 

N

.

N +  + N ? 7 N  N

Afiah kfof yj sh ahaulf, dj nuhrzj

(57)

 

 puhahi shr bmujdjajs y ah hsth ofaf yj sh

kfifkhrïj dj bikfmibtj, ah tjd ojihrj quh tjoebâi sh hikfitrjrïj dj ojmibtua ah dj obsoj kfof sh ouhstrj hi dj hkujkbûi (5:)<

N ? N

 

(5:)

Wfr üdtbof pjrj kfikdubr kfi hd kêdkudf ah nuhrzjs ahd ohkjibsof pfr ohabf ah uij suojtfrbj ah ofohitfs hi hd hsdjeûi 1 sh puhah kjdkudjr sjeh quh su vjdfr hs bmujd j khrf< 1.

Ϋ O1 ? 7

 dj kuêd pfr throbifs yj hstjedhkbafs sh  c  ,

 

c ? 7

 

Wfr ftrf djaf sh hnhktujrê hd kêdkudf hi dj pjrth njdtjith ahd ohkjib ohkjibsof, sof, hs ahkbr, ah dj Wrbohrj kdjsh ahd sbsthoj pjrj kfifkhr dj nuhrzj ah a h kfophisjkbfi y dj

N

. Djs kuêdhs sh dfkjdbzji ah

dj sbmubhith ojihrj hi hd ohkjibsof kfof sh ouhstrj hi dj nbmurj (:1)<

Nbmurj :1. Nuhrzjs ah prbohrj kdjsh.

 

Kfof prbohr pjsf sh tbhih uij suojtfrbj ah ofohitfs hi hd hsdjeûi 5 quhajiaf ah dj sbmubhith ojihrj<

Ϋ O5 ? 7 ∝ D:o+] 3.∝1c3I∝ :¸8o?o7∝ 7.75 o  ? 7  ∝ c75∝ ¸o)∕N 325:3.=;∝58(Noo∝7. ∕N  +  = oo oo

:.

 

(55)

 

 

Afiah sh tbhih kfof bikfmibtj quhajiaf df sbmubhith<

N

, hstj sh ahsphlj ah dj hkujkbûi prhvbjohith hstjedhkbaj

11>;5.5.27 I N ? 11>72.;>8 I∝I ∝ o: + 5;.811 II∝∝ o ? 11>;  ? 11>; N N 11>;5.5.27 I

 

 

Kfof shmuiaf pjsf sh euskj dj

 hstj obsoj sh hikfitrjrê pfr ohabf ah uij suojtfrbj ah

nuhrzjs hi hd hsdjeûi 5, quhajiaf ah dj sbmubhith ojihrj (hkujkbfi (5;))< 5. 

Ϋ N  5 ? 7

 

N + N + N + ] + N ? 7

 

(5;)

Xij vhz hstjedhkbaj dj hkujkbûi pfr ohabf ah ui pfdïmfif vhktfrbjd sh prfkhah j fethihr hd vjdfr ah dj bikfmibtj

  phrf sbi jiths vfdvhr j rhkfrajr djs ohabajs ah dfs ajtfs yj

kfifkbafs pjrj quh sh bopdhohithi hi hd pfdïmfif.

N

N  ? ;7 oo ;>II ?27.1= oo N ? 57283;. 52=;.28 oo 11>;5.27I ? :8.:8.7  N ? 52=;. 28 oo =3.13 I ] ? 52=;.28 oooo?7. I ?7.75>  

 

 

 

 

  Xij vhz hstjedhkbajs djs hskjdjs ah nuhrzjs, sh prfkhah j trjzjr hd pfdïmfif ah nuhrzjs kfof sh ouhstrj hi dj nbmurj (:8).8>.1515  N ? ::7. ::7.;;:: ∝  ∝ 52=; 52=;..28 ooI ? ;537

 

Kfikdusbûi Hi hd prhshith jiêdbsbs ahd ohkjibsof ahd pbstûi, sh bahitbnbkjrfi sus kfopfihiths, sus kdjsbnbkjkbfihs hstrukturjdhs, dfs mrjafs ah dbehrtja hi nuikbûi j sus hdhohitfs y ofvbdbaja, jsï kfof djs abstbitjs vhdfkbajahs, jkhdhrjkbfihs y nuhrzjs j djs quh hstê sfohtbaf, sf ohtbaf, pfr df quh kfi ejsh j tfaj hstj binfrojkbûi fethibaj sh puhah kfikdubr quh j phsjr phsj r ah shr ui ohkjibsof rhdjtbvjohith —kfrtf‟ pfr su kfopfsbkbûi hi hsdjefihs y pjrhs kbihoêtbkfs jahoês ah su —sbopdh‟ nuikbfijobhitf ajaf dfs ofvbobhitfs quh hstâ rhjdbzj , hs ui sbsthoj quh prhshitj

vjrbfs nhiûohifs nïsbkfs ah tbpf vhktfrbjd y kjaj uif ah hstfs vhktfrhs yj shji ah nuhrzj, ah jkhdhrjkbûi f ah vhdfkbaja, kjusji ui hnhktf hsphkïnbkf hi hd pbstûi prfvfkjiaf dfs kfopfrtjobhitfs f ofvbobhitfs hi su nuikbfijdbaja quh yj sh kfifkhi, hstfs puabhiaf shr

 

jprfvhkcjafs hi dj bikdusbûi j ftrfs ohkjibsofs pjrj krhjr sbsthojs quh phrobtji cjkhr nuikbfijr abnhrhiths bivhitfs kfof hs hd kjsf ahd oftfr hi dfs jutfoûvbdhs u ftrjs mrjiahs oêqubijs hi dj vbaj kftbabjij ahd shr cuojif, kfi hddf ahiftjiaf dj bopfrtjikbj quh hsth tbhih hi hd ouiaf ah dj bimhibhrïj ohkêibkj. Hd chkcf ah cjehr puhstf hi prêktbkj tfaj jquhddj thfrïj jaqubrbaj hi dfs ; oûaudfs thoêtbkfs ah dj ojthrbj ah Kbihoêtbkj y Abiêobkj ah Oêqubijs hi hd hstuabf ahd sbsthoj prhshitjaf, jyuaf j pfahr hithiahr tfafs dfs nhiûohifs nïsbkfs bivfdukrjafs hi dj hshikbj obsoj ahd  pbstûi, jd shr abkcj jsbmijturj hd kfobhizf ah dj pjrth ah sbsthojs ohkêibkfs ah dj kjrrhrj ah bimhibhrïj ohkêibkj hdâktrbkj, kfi hsth prfyhktf —sbhoerj‟ dj bopfrtjikbj ah sjehr bithrprhtjr jahoês ah hithiahr kûof sh ddhvji j kjef djs bivhstbmjkbfihs hi dj bivhikbûi y/f ahsjrrfddf ah oêqubijs kfsjs quh sfi cjebtujdhs hi hd trjejlf ah ui bimhibhrf hi hstj rjoj ah dj bimhibhrïj.

 

EBEDBFMUJNÏJ Jiûibof . (5755). Wbstfihs pjrj oftfr y sus tbpfs. :7 ah ojyf ahd 5755, ah cttps