Ecuación de Euler

 

DZWVI K¶

7

XMZGM K¶

WKC^GZ_CHMH HG GL _ML^MHIZ NMOWLXMH HG CKDGKCGZÁM S MZ]WCXGOXWZM G_OWGLM HG CKDGKCGZÁM AGOÍKCOM AÍ]WCKM_ BCHZÍWLCOM_ OCOLI C-:6:=

K¶

: NGOBM (67/6?/:6:=) OIZZGI CK_XCXWOCIKML CK_XCXWOCIKML

G_XWHCMKXG Jikcllm Jikcllm, Jgkcdki Mlgxmkhgr Nlirgs ^gkturm, Nrmkolck Csmmo

= : ?

 jj=7663Fugs.ghu.sv nv=>663Fugs.ghu.sv

Vgrgz Vgrgz, @ulci Ogsmr

pp=86?8Fugs.ghu.sv

HG_OZCVOCßK HG LM XMZGM0 XMZGM 0 sg rgmlczmrí uk rgsuagk hg lm sgoocÿk ?.:, bmstm gl tgam hg trcíkdulis hg vgliochmh hgl lcjri turjiaíquckms bchríulcoms hg Olmuhci Amtmcx.

HG_MZZILLI0   HG_MZZILLI0 Lm gkgrdám qug gl nluchi cktgromajcm oik gl rihgtg pughg sgr hg his olmsgs0 •

hg prgscÿk i    Gkgrdám Gkgrdám ockãtcom.

•

Lm rglmocÿk gktrg lm gkgrdám hg prgscÿk cktgromajcmhm gk gl rihgtg m lm gkgrdám titml gs uk pmríagtri hg drmk capirtmkocm pir su rgpgrouscÿk gk hcsgýi y nukocikmacgkti hg lms turjiaíquckms bchríulcoms, y sg hgkiackm drmhi hg rgmoocÿk. Lm goumocÿk hg Gulgr i goumocÿk nukhmagktml hg lms turjiaíquckms gstm lcactmhm pir oumtri bcpÿtgscs qug sik0 =.  =.  :.  :.  ?.  ?.  8.  8. 

Zãdcagk pgramkgktg. Nluchi chgml. Nlu`i crritmocikml. Aãtihi ukchcagkscikml.

Vmrm ukm turji amquckm dgkgrmlczmhm ncdurm =. Lm trmygotircm hg lm pmrtáoulm gk gl rihgtg oikstctuyg uk nclmagkti hg oirrcgktg ml qug lg pihgais mplcomr gl tgirgam hg lm omktchmh hg aivcacgkti. Lis aiagktis sg tiamk gk rglmocÿk ml g`g hg lm turjiaíquckm. Gl aiagkti hg lms oiapikgktgs rmhcmlgs y mxcmlgs m lm gktrmhm y smlchm sik kulis, gl aiagkti titml sgrí cduml ml oirrgspikhcgktg m lm vgliochmh pgrcnãrcom  1  ois⍰.

(  √ )  √ 1 (  √   ) 1 (  1 ∥ (  √   )  -hA(rgmoocik)0 aiagkti hg lms nugrzms gxtgrcirgs qug motðmk sijrg gl nluchi mcslmhi. hA(moocik)0 aiagkti hg lms nugrzms qug gl nluchi mcslmhi g`grog sijrg gl gxtgrcir.

 

r=, r:0 rmhcis y jrmzis hg aiagkti hg lms oiapikgktgs pgrcnãrcoms O=u, Ou:. hD0 dmsti amscoi m trmvãs t rmvãs hgl nclmagkti. Gl sgdukhi acgajri hg lm goumocÿk pughg cktgdrmrsg sc sg tiamk gk ougktm lms 8 bcpÿtgscs qug lcactmk ml tgirgam gktikogs tgkhrgais0

 1 (  √   )   1 (  √   )  A gs gl aiagkti hgl nluchi sijrg gl gxtgrcir y gk pmrtcoulmr sijrg gl rihgtg. Gs gl aiagkti g`grochi sijrg lis mlmjgs y sijrg gl nluchi gxtgrcir m lm gktrmhm y smlchm hgl rihgtg, hikhg sg gstmjlgogk lms supgrncocgs hg oiktril. Lm pitgkocm agoíkcom trmksactchm pir gl nluchi ml rihgtg sgrí.

 1 ⍷ ⍷ 1  ( ⍷ √  ⍷ ) 1  (  √   )  _c sg cdumlm lm pitgkocm agoíkcom m gl smlti i oiksuai hg pitgkocm hg nluchi kgogsmrci pmrm trmksactcr hcobm pitgkocm.

 1      1   1  ( √   )  Lm kitmocÿk Su∛  sg usmrí pmrm gxprgsmr qug lm gkgrdám ijtgkchm oirrgspikhg m lm tgirám ukchcagkscikml hg lm oirrcgktg pgrngotmagktg ducmhm i sgm oik cknckcti kuagri hg mlmjgs gk gl rihgtg, sg ijtcgkg lm prcagrm niram hg lm goumocÿk hg Gulgr.

∛ 1   √    ∛ 1 ∛ 1  √     (=)  = ∛ 1 (  √  ) (:)   ∛ 1   √     (?)  ∛ 1 = (  √  ) (8)   Gk = y : sg rgprgsgktm lm gkgrdám oghchm pir gl nluchi ml rihgtg. S gk ? y 8 sg rgprgsgktmk lm gkgrdám mjsirjchm pir gl nluchi gk gl rihgtg. r ihgtg. Xrcíkdulis hg vgliochmh Oiai sg augstrm gk lm ncdurm : gk su pmsi pir gl rihgtg hg ukm jiajm ukm pmrtáoulm hg nluchi hgsorcjg his trmygotircms =) trmygotircm rglmtcvm0 lm pmrtáoulm scdug gl oiktirki hg lis mlmjgs :) trmygotircm mjsilutm0 lm pmrtáoulm sg augvg `ukti oik lis mlmjgs hgl rihgtg.

⃔1  √⃔

(7)  

 

 0 vgliochmh mjsilutm hgl nluchi ⃔ 0 vgliochmh hgl nluchi oik rglmocÿk ml rihgtg ⃔ 0 vgliochmh mjsilutm hgl rihgtg Gl trcmkduli niramhi pir lis ? vgotirgs gk omhm pukti x hg lm turjiaíquckm sg pughg hgnckcr uk trcmkduli hg vgliochmh tml qug

⃔1 ⃔ √  ⃔   Gk lm ncdurm ? sg augstrm tihm lm ckniramocÿk qug pripirocikmk lis trcíkdulis hg vgliochmh m lm gktrmhm, pukti = y smlchm, pukti : gk lis mlmjgs, gk lm ncdurm 8 sg augstrmk lms kirams sgduchms pmrm lm oikstruoocÿk hg lis trcíkdulis hg vgliochmh. Hg lm ncdurm ? mplcomkhi lgy hg oisgkis m majis trcíkdulis hg vgliochmh.

  1   +   √ :  ois⍰ 1   +   √ :     1   +   √ : ois⍰ 1   +   √ : 

S mhgaís

=   1 (  +   √   )  : =   1 (  +   √   )  : sá sustctucais lms his ðltcams gxprgscikgs ijtgkchms gk lms goumocikgs = y 8 ijtgkhrgais lm sgdukhm niram hg lm goumocÿk hg Gulgr.

 √     √     √   ∛ 1 ½( + + )  : : : 

∛ 1

½( ½(





√ 

:

+ 





√ 

:

+ 



√ 

:

) 

OIKOLW_CIKG_0   Lm goumocÿk hg Gulgr gstmjlgog gl cktgromajci hg gkgrdám gktrg gl rihgtg y gl nluchi gk ukm turjiaíquckm bchríulcom, hgjchi m lm vmrcmocÿk hg lm omktchmh hg aivcacgkti.   Lm goumocÿk hg Gulgr pughg rgsilvgrsg scgaprg qug sg tiagk gk ougktm lms oumtri bcpÿtgscs qug lm lcactmk.

•

•

 

MKGRI_

Ncdurm =

Ncdurm :

 

Ncdurm ?

o0 vgliochmh mjsilutm hgl nluchi gk uk pukti hgl rihgtg W0 vgliochmh mjsilutm hgl rihgtg gk gsg pukti T0 vgliochmh rglmtcvm hgl nluchi oik rgspgoti ml mlmjg

⍰0 íkduli qug niramk lis vgotirgs  ⃔  κ0 íkduli qug niramk lis vgotirgs⃔wy

(√u ⃔) 

ou0 oiapikgktg pgrcnãrcom hg lm vgliochmh mjsilutm oa0 oiapikgktg agrchcikml hg lm vgliochmh mjsilutm

Ncdurm 8

 

Gl vgotir⃔ sg hcju`mrí hcrcdchi hg czqucgrhm m hgrgobm y lis vgotirgs  ⃔ rgprgsgktmtcvis hg lms vgliochmhgs hgl nluchi oik uk ircdgk oiaðk, gk oumlqucgrm hg lms nirams rgprgsgktmhms gk (m). Hgktri hg gstg oikvgkci, pmrm lis trcíkdulis hg gktrmhm y smlchm sg utclczmk oumlqucgrm hg lms trgs nirams0 =.  =.  (j) hg niram hgsmrrillmhm. :.  :.  (o) hg niram pilmr. ?.  ?.  (h) niram oikhgksmhm.