Résumé de La Cinématique Du Solide
November 20, 2022 | Author: Anonymous | Category: N/A
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Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 0/01
Lmbík`tmqug ju scimjg mbjíacrk`nig
0) CNFGLZMA................... CNFGLZMA.............................. ....................... ....................... ...................... ...................... ....................... ....................... ...................... ................... ..........< ..<
>) ^GAG^GBZMGI (G\X@LG-ZGKX\). ............. .......................... .......................... .......................... .......................... ......................... ..............< ..< >0) BCZMCB JG ^GAG^GBLG \X@ZM@IG. ........ ............... ............... ............... ............... ............... ............... ............... ............... ............... ............... .............. ...... >) BCZMCB JG ^GAG^GBLG ZGKXC^GIIG. ........ ............... ............... ............... ............... ............... ............... ............... ............... ............... ............... ........ 808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 1/01
:) L`s oíbír`i.
j x Cb jíkcbtrg jg i` kækg a`ïcb qug sm x 4 gst ub vgltgur ubmt`mrg jg N 4 `icrs `icrs 4 4 / < x 4 jt ^
<
Bg f`k`ms utmimsgr lgttg rgi`tmcb pcur jgs vgltgurs bcb-ubmt`mrgs.
\m vcus `vgzcunimí ig l`s p`rtmluimgr p`og prílíjgbtg, i` acrkuig ju l`s oíbír`i acbltmcbbg tcut ig tgkps 6 j x 0 x z x y 0 0/ 8 0 8 0 jt
^ 8
j y 0 y z y x0 0/ 8 0 8 0 jt ^ 8
j z 0 8 z z z 0/ 8 0 8 0 jt ^ 8
::) ^gi`tmcb gbtrg igs jírmvígs tgkpcrgiigs j”ub vgltgur p`r r`ppcrt jgux rgpärgs 6 vgltgur Acrkuig jg Nccr. ^gprgbcbs i` è jírmvíg tgkpcrgiig jg bctrg ju p`r`or`pdg :> gt `ppimqucbs i` acrkuig ju p`r`or`pdg : 6
8
8
j x0 j y0 j z0 jW n y0 n l z0 l ` x0 ` jt ^ jt ^ jt ^ jt ^ 8
`vgl
8
j x 0 0/ 8 x 0 jt ^
8
j y 0 0/ 8 y 0 jt ^
8
j z 0 0/ 8 z 0 jt ^ 8
jW ` x0 n y0 l z0 0/ 8 (` x0 n y0 l z0) jt ^
qum jgvmgbt
8
0 0 ` x n y l z0 gb rgk`rqu`bt qug jW jt ^
l`r
x0, y0
gt z 0 amxgs j`bs ^0, cb cntmgbt 6
0
jW j W 0/8 W jt ^8 jt ^ 0
Acrkuig jg Nccr qum b'gst p`s è lcbb`âtrg, k`ms qum sgr` ubmqugkgbt utmig lckkg íiíkgbt jg lcurs pcur jíkcbtrgr j”`utrgs rgi`tmcbs…
KX\M-XL\M
\lmgblgs Mbjustrmgiigs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og ?/01
7) Lmbík`tmqug ju scimjg. 70) Jíambmtmcb ju scimjg mbjíacrk`nig. Zcus igs scimjgs sg jíacrkgbt icrsqu”mis sunmssgbt jgs ld`rogs. Lgs jíacrk`tmcbs jípgbjgbt jgs ld`rogs, jgs jmkgbsmcbs gt jg i` k`tmärg. Jíambmr ig kcuvgkgbt j”ub scimjg jíacrk`nig gst ub prcniäkg lckpigxg. J`bs jg bcknrgux l`s igs jíacrk`tmcbs scbt suaams`kkgbt pgtmtgs pcur qug i”cb pumssg igs bíoimogr. @amb jg smkpimamgr i”ítujg, cb `ssclmg `icrs `u scimjg rígi \ ig kcjäig smkpimamí ju scimjg mbjíacrk`nig tgi mbjíacrk`nig tgi qug 6 @N Ltg . t , @ \, N \, Igs`llgptgr` scimjgs jcbt i` acbltmcb jg sg jíacrkgr jg tcrsmcb, …) scbt gxlius jg lgttg jíambmtmcb. Cb j`bs lg lcursgst ig tgrkg jg scimjg (rgsscrts, pcur scimjgn`rrgs mbjíacrk`nig. I` lmbík`tmqug j”ub scimjg mbjíacrk`nig gb kcuvgkgbt, pcssäjg jgs p`rtmlui`rmtís qum pgrkgttgbt ubg ítujg smkpimamíg ju kcuvgkgbt oicn`i s`bs `vcmr è ítujmgr ld`qug pcmbt mbjmvmjugiigkgbt (lckkg pcur i` lmbík`tmqug ju pcmbt). I` kmsg gb ívmjgblg jg lgs p`rtmlui`rmtís gst i”cnfgltma jg lgttg p`rtmg.
7>) Zr`fgltcmrg j”ub pcmbt `pp`rtgb`bt è ub scimjg 6 Z K > /0 . Xcur ætrg rmocurgux, cb p`rigr` jg 6
- tr`fgltcmrg j”ub pcmbt, - kcuvgkgbt j”ub scimjg.
Xcur jítgrkmbgr ubg tr`fgltcmrg, mi a`ut `v`bt tcut lcbb`âtrg ig kcuvgkgbt gbtrg igs > scimjgs ítujmís. Gxgkpigs 6
Zr`fgltcmrgs jg pcmbts `pp`rtgb`bt è ub scimjg gb kcuvgkgbt jg tr`bsi`tmcb rgltmimobg. Igs tr`fgltcmrgs scbt jgs sgokgbts jg jrcmtg.
Zr`fgltcmrgs jg pcmbts `pp`rtgb`bt è ub scimjg gb kcuvgkgbt jg tr`bsi`tmcb lmrlui`mrg. (gxgkpig 6 n`i`m j”ub gssumg-oi`lg j”`utcnus lm-jgsscus, cu or`bjg rcug j'ubg aætg acr`mbg) Igs tr`fgltcmrgs scbt jgs `rls jg lgrlig jg kækg r`ycb.
Zr`fgltcmrgs jg pcmbts `pp`rtgb`bt è ub scimjg gb kcuvgkgbt jg rct`tmcb `utcur j”ub `xg amxg. (gxgkpig 6 n`i`m j”ub gssumg-oi`lg jg vcmturg lm-jgsscus) Igs tr`fgltcmrgs scbt jgs `rls jg lgrlig jg kækg lgbtrg (j`bs ig pi`b) cu jg kækg `xg (j`bs i”gsp`lg). Z N 0n`i`m / p`rg nrmsg
Z N > n`i`m / p`rg nrmsg
Gssumg-oi`lg jg vcmturg
Gssumg-oi`lg j”`utcnus
> µ (kækg sm lg b”gst p`s ig l`s j`bs Jítgrkmbgr Z K >/0 >/ 0 smobmamg j”cntgbmr Z K /0 gb lcbsmjír`bt qug « K i` rí`imtí). Lglm pgut gbtr`âbgr amltmvgkgbt ig nicl`og jg lgrt`mb kcuvgkgbt (vcmr ZJ8=).
KX\M-XL\M
\lmgblgs Mbjustrmgiigs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 4/01
7 /0 . 7 `tt`ldí è ub rgpärg ^ >, gb kcuvgkgbt p`r r`ppcrt `u rgpärg ^0. Cb bctg Q K >/0 i` vmtgssg ju pcmbt K `pp`rtgb`bt `u scimjg > j`bs scb kcuvgkgbt p`r r`ppcrt `u rgpärg ^ 0. I”gbsgknig I”gbsgkni g jgs vgltgurs vmtgssgs jgs pcmbts ju scimjg > gst `ppgií ld`kp jgs vgltgurs vmtgssgs. Gxgkpigs lm-jgssus cý `u i”cbrgpärg pgut ju cnsgrvgr ig ld`kp jgs vgltgurs vmtgssgs jgs pcmbts ju n`i`m j`bs scb kcuvgkgbt p`r r`ppcrt p`rg-nrmsg.
7) ^gi`tmcb ju ld`kp jgs vgltgurs vmtgssgs jgs pcmbts `pp`rtgb`bt è ub scimjg. \cmt ub scimjg 0 gb kcuvgkgbt p`r r`ppcrt è ub rgpärg ^ 8. \cmt @ gt N jgux pcmbts ju scimjg 0. j @N j @N Cb ` 0/8 @N (acrkuig jg Nccr) `vgl 6 jt 8 jt 0
j @N @N amxg j`bs ^ 0 jcbl 8 jt 0
j C8N j C8 @ j @N @N @C8 C8 N C8 N C8 @ jcbl QN / 8 Q @ /8 jt 8 jt 8 jt 8
Cb cntmgbt 6 QN / 8 Q@ / 8 0/ 8 @N Xcur nmgb spílmamgr qug lgttg rgi`tmcb b”gst v`i`nig qug pcur jgs pcmbts `pp`rtgb`bt `u kækg scimjg mbjíacrk`nig, mlm ig scimjg 0, cb bctg 6 QN0/ 8 Q@0/ 8 0/8 @N
cu QN0/ 8 Q@0/ 8 N@ 0/ 8
7 gb kcuvgkgbt p`r r`ppcrt è ub rgpärg ^ 0, ium-kækg gb kcuvgkgbt p`r r`ppcrt è ub rgpärg ^8. \cmt ub pcmbt X ju scimjg >, `icrs
QX> / 8
QX / 8 " X > "
jC X Q X >/8 8 jt 8
jC C jC X Q X >/8 8 0 0 jt 8 jt 8
jC X QX> /8 QC00/ 8 0 0/8 C0X (utmims`tmcb jg i` acrkuig jg Nccr) jt 0
QX> /8 QC00/ 8 QX >/0 0/8 C0X
QX> /8 QX>/0 QC00/ 8 XC0 0/ 8
QX>/ 8 QX>/0 Q X 0/ 8
pums gb utmims`bt i` rgi`tmcb ju ld`kp jgs vgltgurs vmtgssgs j”ub scimjg, cb cntmgbt 6
(rgi`tmcb qum bcus r`ppgiig i` acrkuig jg Ld`sigs)
7:>) Lckpcsmtmcb jgs vgltgurs vmtgssgs jg rct`tmcb 6
>/ 8 >/0 0/ 8
.
\cmt < rgpärgs sp`tm`ux (^0, ^> gt ^/0 W jt ^ jt ^ 0
>
Gb `fcut`bt kgknrg è kgknrg, mi vmgbt 6
jW
jW > /0 0/ 8 W
Cr, cb pgut ío`igkgbt ílrmrg qug
jt ^8 jt ^ > jW j W >/ 8 W (acrkuig jg Nccr gbtrg igs scimjgs 8 gt >) jt ^8 jt ^ >
X`r mjgbtmaml`tmcb, cb jíjumt i` rgi`tmcb jg lckpcsmtmcb jgs vgltgurs vmtgssgs jg rct`tmcb 6 rct`tmcb 6
>/ 8 >/0 0/8
7: /8 Q>/0 Q 0/ 8 .
>/ 8 >/0 0/ 8 Bcus `vcbs ít`nim qug 6 . Q Q X>/ 8 X>/0 Q X 0/ 8
@mbsm Q>/ 8
Q>/0 Q 0/8
@ttgbtmcb 6 pcur sckkgr jgs tcrsgurs, lgs jgrbmgrs jcmvgbt ætrg gxprmkís `u kækg pcmbt. i` lckpcsmtmcb jg kcuvgkgbt pgut a`mrg mbtgrvgbmr b rgpärgs mbtgrkíjm`mrgs 6 Qb / 8 Qb / b 0 ... Q 0/ 8 .
KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 08/01
77) Jík`rldg jg jítgrkmb`tmcb `b`iytmqug jg i` vmtgssg j”ub pcmbt `pp`rtgb`bt è ub scimjg. Mi gxmstg > kítdcjgs pcur jítgrkmbgr ub vgltgur vmtgssg j”ub pcmbt `pp`rtgb`bt è ub scimjg 6 \m N `pp`rtmgbt rígiigkgbt è >
X`r jírmv`tmcb vgltcrmgiig
QN>/ 8 QN / 8 " N > "
\m Nbt p`s b”`pp`rtmg b”`pp`rtmgbt rígiigkgbt è >
" N > " b”`ppcrtg `ulubg lcbjmtmcb suppiíkgbt`mrg " N > " `ppcrtg jgs lcbjmtmcbs suppiíkgbt`mrgs
QN>/ 8
QN> /0 Q N0/ 8
gst ubg tr`bsi`tmcb rgltmimobg
(gx 6 ig kcuvgkgbt jg >/0 gst ubg tr`bsi`tmcb)
QN / 8 " N > " jC8 N " N > " jt 8
QN>/ 8
(p`r`kätrgs v`rm`nigs qum jgvmgbbgbt lcbst`bts)
\m ub jgs kcuvgkgbts íiíkgbt`mrgs X`r Lckpcsmtmcb jgs gst ubg rct`tmcb vgltgurs vmtgssgs, sumvmg jg (gx 6 ig kcuvgkgbt jg 0/8 gst ubg rct`tmcb i` ^gi`tmcb ju ld`kp jgs jg lgbtrg @) vgltgurs vmtgssgs jgs pcmbts \m ub jgs kcuvgkgbts íiíkgbt`mrgs `pp`rtgb`bt è ub scimjg
jC N QN>/ 8 Q N /8 8 jt 8
QN0/ 8
Q@0/ 8 N@ 0/ 8
jC N QN>/0 QN /0 " N > " 0 " N > " jt 0
71) Ld`kp jgs vgltgurs `llíiír`tmcbs jgs pcmbts `pp`rtgb`bt è ub scimjg 6 K >/>/00 .
\cmt jgux pcmbts @ gt N `pp`rtgb`bt è ub scimjg 0 gb kcuvgkgbt p`r r`ppcrt è ub rgpärg ^ 8. Bcus `vcbs ít`nim 6 QN0/ 8 Q@0/ 8 N@ 0/ 8 Jírmvcbs lgttg gxprgssmcb p`r r`ppcrt `u tgkps j`bs ^8. jQN0/ 8 jQ j 0/ 8 jQ@0/ 8 j N@ 0/8 N@ jt 8 jt jt jt 8
8
j N@ j 0/8 \cmt N0/ 8 @0/ 8 0/ 8 N@ 0/ 8 N@ jt jt 0
8
@N gst amxg j`bs ^ 0.
8
J”cý
0/8 N0/ 8 @0/ 8 0/ 8 N@ 0/ 8 N@ j
jt 8
Ig ld`kp jgs vgltgurs `llíiír`tmcbs jgs pcmbts `pp`rtgb`bt è ub scimjg bg pgut p`s ætrg jílrmt p`r ub tcrsgur l`r lg b”gst p`s ub ld`kp jg kckgbt ( KN K @ N@ ^ , mlm N0/ 8 @0/ 8 N@ 0/ 8 ). @mbsm, pcur jítgrkmbgr ubg `llíiír`tmcb, bcus sgrcbs cnimoís è ld`qug acms jg jírmvgr ig vgltgur vmtgssg.
KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 00/01
1) Lmbík`tmqug ju lcbt`lt pcbltugi. 10) ^cuigkgbt, pmvctgkgbt, oimssgkgbt. Gb ub pcmbt jg lcbt`lt X gbtrg jgux scimjgs \0 gt \>, cb jíambmt tcufcurs 6 - ub pi`b t`bogbt lckkub`ux jgux scimjgs, - ubg bcrk`ig `u lcbt`lt b .
>/0 Gb X, cb jíambmt ig tcrsgur lmbík`tmqug 6 Q >/0 Q X >/0 X
b .b t 0.t0 t > .t > J`bs ub rgpärg icl`i jg lcbt`lt (X , b, t0,t> ) 6 Q >/0 8.b Qt0.t0 Qt > .t> X
8 lcrrgspcbj è ub pmvctgkgbt `utcur jg i` bcrk`ig lckkubg jg \>/\0.
•
b .b
•
t 0.t0 t > .t >
8 lcrrgspcbj è ub rcuigkgbt j`bs ig pi`b t`bogbt jg \>/\0.
• QX >/0 .b 8 mbjmqug ig k`mbtmgb k`mbtmgb jg lcbt`lt lcbt`lt s`bs píbítr`tmc píbítr`tmcb. b.
• Qt0.t0 Qt > .t> 8 lcrrgspcbj è ub oimssgkgbt gb X j`bs ig pi`b t`bogbt jg \>/\0.
@mbsm, gb ub pcmbt pcmbt jg lcbt`lt lcbt`lt X gbtrg jgux jgux scimjgs \0 gt gt \>, Q X >/0 gst `ppgiíg vmtgssg jg oimssgkgbt. I` vmtgssg jg oimssgkgbt `pp`rtmgbt `u pi`b t`bogbt lckkub `u lcbt`lt. ^gk`rqug 6 igs lckpcs`btgs jg pmvctgkgbt gt jg rcuigkgbt ju vgltgur rct`tmcb jípgbjgbt ju pcmbt jg lcbt`lt lcbtr`mrgkgbt `u vgltgur rct`tmcb qum gst mbjípgbj`bt ju pcmbt lcbsmjírí.
1>) Zr`fgltcmrg gt vmtgssg gb ub pcmbt oíckítrmqug jg lcbt`lt Xcmbts lcãblmjgbts. Mi gst jíiml`t jg s`vcmr lg qu'mi sg p`ssg gb ub pcmbt jg lcbt`lt X l`r cb jmstmboug < pcmbts lcãblmjgbts è lcãblmjgbts è i”mbst`bt t 6 - X \0 pcmbt imí è \0, - X \> pcmbt imí è \>, X pcmbt oíckítrmqug jg lcbt`lt - X \0 gt \ > pcmbt oíckítrmqug jg lcbt`lt. X rcug
X sci
Gx 6 Icrsqu”ubg rcug sg jípi`lg sur ig sci, `u pcmbt jg lcbt`lt X gbtrg i` rcug gt ig sci, cb jmstmboug 6 - X sci 6 l”gst ig or`vmiicb amxg ju nmtukg, s` tr`fgltcmrg p` r r`ppcrt `u sci gst ub pcmbt. - X rcug 6 mi gst `tt`ldí è i` rcug, s` tr`fgltcmrg p`r r`ppcrt `u sci gst ubg lylicãjg. - X 6 pcmbt oíckítrmqug jg lcbt`lt, s` tr`fgltcmrg `pp`rtmgbt `u sci (giig rgprísgbtg igs pcsmtmcbs sullgssmvgs prmsgs p`r ig pcmbt oíckítrmqug jg lcbt`lt gbtrg i` rcug gt ig sci).
@mbsm, pcur jítgrkmbgr i` tr`fgltcmrg j”ub pcmbt oíckítrmqug jg lcbt`lt lcbt`lt j`bs ub rgpärg qugilcbqug, cb cb jítgrkmbg j'`ncrj scb vgltgur pcsmtmcb j`bs pcsmtmcb j`bs lg rgpärg. Jg kækg, pcur l`iluigr ubg vmtgssg gb ub pcmbt oíckítrmqug jg lcbt`lt, mi bg a`ujr` F@K@M\ utmimsgr i` jíambmtmcb (lmbík`tmqug ju pcmbt `vgl igs lcbjmtmcbs " X \0 " cu " X \ > "), l`r mi gst mkpcssmnig jg tr`jumrg lgs lcbjmtmcbs. Jgux kítdcjgs pguvgbt ætrg `icrs utmimsígs pcur l`iluigr lgttg vmtgssg 6 lcbjmtmcbs. Jgux QX> /0 QX> / 8 Q X 0/ 8 utmims`tmcb jg i` lmbík`tmqug ju scimjg (lckpcsmtmcb jgs vgltgurs vmtgssgs, sumvmg jg i` rgi`tmcb ju ld`kp jgs vgltgurs vmtgssgs jgs pcmbts `pp`rtgb`bt è ub scimjg “ Qcmr p`rtmg 7:) QX> / 0 QX /0 Q X / > (jílckpcsmtmcb, pums l`ilui jg Q X /0 gt Q X /> p`r i` lmbík`tmqug ju pcmbt)
1 rcuig s`bs oimssgr sur \0 gb X sm i` vmtgssg jg oimssgkgbt gst buiig 6 Q X >/0 8 . Zcut pcmbt jg ^\O gst ub LM^ (vcmr p`r`or`pdg p`r`or`pdg sur igs LM^).
KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 0>/01
?) Kcuvgkgbts p`rtmluimgrs. ?0) Kcuvgkgbts jg tr`bsi`tmcb. Wb scimjg \> gst gb kcuvgkgbt jg tr`bsi`tmcb p`r r`ppcrt è ub rgpärg ^0 sm gt sguigkgbt sm scb vgltgur rct`tmcb >/0 gst bui. \gicb i` icm ju ld`kp jgs vgltgurs vmtgssgs, lglm mkpimqug qug tcus igs pcmbts ju scimjg cbt kækg vgltgur vmtgssg è i”mbst`bt t. K`ms `ttgbtmcb 6 lg vgltgur vmtgssg b”gst p`s bílgss`mrgkgbt lcbst`bt j`bs ig tgkps. 8 I` acrkg ju tcrsgur lmbík`tmqug sgr` jcbl 6 (qugiqug scmt ig pcmbt jg ríjultmcb) Q >/0 >/0 Q X X >/0 8 smobmamg `ussm qug N0;N> (kækg crmgbt`tmcb), k`ms `ttgbtmcb ^0 ^> l`r igs crmombgs sg jípi`lgbt.
Mi gxmstg piusmgurs typgs jg kcuvgkgbt jg tr`bsi`tmcb sgicb i` b`turg jg i` tr`fgltcmrg 6 - tr`bsi`tmcb rgltmimobg 6 rgltmimobg 6 igs tr`fgltcmrgs jgs pcmbts scbt jgs sgokgbts jg jrcmtg, - tr`bsi`tmcb lmrlui`mrg lmrlui`mrg 6 igs tr`fgltcmrgs jgs pcmbts scbt jgs `rls jg lgrlig jg kækg r`ycb (vcmr lm-lcbtrg, i` or`bjg rcug j”ubg aætg acr`mbg), - tr`bsi`tmcb lurvmimobg lurvmimobg 6 igs tr`fgltcmrgs jgs pcmbts jílrmvgbt jgs lcurngs qugilcbqugs.
?>) Kcuvgkgbts jg rct`tmcb. Wb scimjg scimjg \> gst gst gb kcuvgkg kcuvgkgbt bt jg rct`tmc rct`tmcb b `utcur `utcur j'ub j'ub `xg ( ) p`r r`ppcrt è lmbík`tmqug gst jg i` acrkg acrkg sumv`btg sumv`btg g gb b tcut pcmbt L jg i'`xg ( ) 6 Q >/0
Xcur
ub rgpärg ^0, sm ig tcrsgur
>/0 8 L ( )
tcut pcmbt L ( ) , cb ` Q L 8 (vmtgssg buiig sur i”`xg jg rct`tmcb) rct`tmcb) >/0
llcim cimbí bí`mr `mrg g è i'`xg i'`xg ( ) , `ppgií `ussm `xg mbst`bt`bí jg rct`tmcb (cu rct`tmcb (cu `xg lgbtr`i ju tcrsgur). Zcus igs pcmbts jg \> cbt ubg tr`fgltcmrg lmrlui`mrg / ^0 (`rls jg lgrlig jg lgbtrg ub pcmbt `pp`rtgb`bt è i”`xg ( ) ). \cmt K ( ) gt L ig prcfg prcfgtí tí crtdc crtdcocb ocb`i `i jg jg K sur sur ( ) , cb ` 6 >/0 gs gstt
QK>/0 QL >/0 KL >/0 KL > /0
>/0 , cb ` QK > /0 Lckkg KL
KL . > /0 `vgl KL ^ gt >/0
QK >/0 KL
QK >/0 .^
Q K >/0 prcpcrtmcbbgiig è KL
Ig vgltgur vmtgssg jg tcut pcmbt bcb smtuí sur ( ) gst t`bogbt è s` tr`fgltcmrg lmrlui`mrg gt ` ubg bcrkg prcpcrtmcbbgiig è i` jmst`blg síp`r`bt ig pcmbt jg i”`xg mbst`bt`bí jg rct`tmcb. Cb p`rig `icrs jg ríp`rtmtmcb imbí`mrg jgs vmtgssgs jgs vmtgssgs jgs pcmbts `pp`rtgb`bt è ub scimjg gb rct`tmcb.
Igs vgltgurs vmtgssgs jg pcmbts smtuís è ubg kækg jmst`blg jg () cbt kækg bcrkg
I` bcrkg gst prcpcrtmcbbgiig è i` jmst`blg síp`r`bt síp`r`bt K jg L
?808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 0 gb kcuvgkgbt i”ub p`r r`ppcrt è i”`utrg. Ig kcuvgkgbt jg \> p`r r`ppcrt è \0 gst jmt pi`b, cu pi`b sur pi`b, s”mi gxmstg ub pi`b > imí è \> qum rgstg lcbst`kkgbt gb lcãblmjgblg `vgl ub pi`b 0 imí è \0. Lg pi`b gst `ppgií pi`b jg oimssgkgbt.
40>) X`rtmlui`rmtís j”ub kcuvgkgbt pi`b sur pi`b.
gt \0, tgis qug igs pi`bs
8 (C, x , y ) gt 0(C0 , x0 , y 0 ) scmgbt
lcãblmjgbts. Cb
` jcbl 6 z z 0 . Ig p`r`kítr`og jg i` smtu`tmcb jg \0 p`r r`ppcrt è \8 bílgssmtg j”mbtrcjumrg > p`r`kätrgs jg pcsmtmcb ( xC0, y C0) gt 0 p`r`kätrg j”crmgbt`tmcb () .
x0
y0
\cmt ^8 (C, x, y, z ) gt ^0(C0, x0, y0, z0) , jgux rgpärgs imís rgspgltmvgkgbt è \8 y
C0 y C0
C
x
x C0
Ig tcrsgur lmbík`tmqug ju kcuvgkgbt pi`b sur pi`b jg \0 p`r r`ppcrt è \8 p`r`iiäigkgbt `u pi`b ( x, y ) s”ílrmt 6 8 xC0 8 x K 0/8 .z Q 0/ 8 8 y 8 yC0 K C0 8 ( x,y,z ) K 8 ( x,y,z ) QC00/ 8 xC0.x yC0.y C 0 Lcbliusmcbs 6 ig vgltgur rct`tmcb gst pgrpgbjmlui`mrg `ux pi`bs 8 gt 0 . igs vgltgurs vmtgssgs scbt tcus p`r`iiäigs `ux pi`bs 8 gt 0 . ig kcuvgkgbt pi`b sur pi`b gst i` lcknmb`mscb j”ubg tr`bsi`tmcb gt j”ubg rct`tmcb.
4>) @v`bt`ogs gt mblcbvíbmgbts jg i` lmbík`tmqug or`pdmqug p`r r`ppcrt è i` lmbík`tmqug `b`iytmqug. @v`bt`og 6 Kítdcjg pius r`pmjg. Mblcbvíbmgbts 6 Kítdcjg utmimsíg sguigkgbt pcur jgs kcuvgkgbts pi`b sur pi`b. I` sciutmcb jítgrkmbíg gst v`i`nig sguigkgbt j`bs i` pcsmtmcb jg i` amourg (sm i”cb scud`mtg ubg vmtgssg j”ub pcmbt ju scimjg j`bs ubg `utrg pcsmtmcb, mi a`ut rga`mrg ig sldík` gt i` lcbstrultmcb or`pdmqug…). Kítdcjg kcmbs prílmsg.
4 kcuvgkgbts j”gbtríg. I”íqumprcfgltmvmtí gt ig LM^ scbt utmimsís pcur jítgrkmbgr ubg vmtgssg j”ub pcmbt j”ubg pmälg `y`bt ub kcuvgkgbt qugilcbqug p`r r`ppcrt `u nîtm (l'gst-è-jmrg qug l”gst bm ubg rct`tmcb, bm ubg tr`bsi`tmcb).
KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
4/0 gt Q N 0/8 .
@ icrs cb pgut jíjumrg jíjum rg Q N >/8 6
- > jmrgltmcbs (Q N >/8 ) gt (Q N 0/8 ) .
@ icrs cb pgut jíjumrg jíjum rg Q N >/8 gt Q N 0/8 6
^gk`rqug j`bs i”gxgkpig lm-jgsscus, ig kvt jg 0/8 gst ubg tr`bsi`tmcb gt ig kvt jg >/0 gst ubg rct`tmcb jg lgbtrg @. jg ` nmgb > lckpcs`btgs 6 ubg, mssug i` @mbsm Q N >/8 tr`bsi`tmcb ( Q N 0/8 ) gt i”`utrg, mssug jg i` rct`tmcb ( Q N >/0 )…
0
Cb lckpcsg gb N 6 QN> /8 QN>/0 Q N0/ 8 .
Cb rgpcrtg ubg jmrgltmcb lcbbug è i”`utrg gxtríkmtí ju vgltgur lcbbug, gt cb tr`lg ig trm`boig jg lckpcsmtmcb jgs vgltgurs vmtgssgs. \umv`bt ig ldcmx jg i` jmrgltmcb è jípi`lgr, lcbstrultmcbs `ncutmss`bt `u kækg rísuit`t pguvgbt ætrg >gaagltuígs 6 (QN> / 8 )
>
QN 0/ 8
8
QN > / 8 @ L QL 0/ 8
QN > / 0 N
QN > / 8
(QN0/ 8 )
QN > / 0
N
(QN> / 8 )
CW
QN 0/ 8
QN > / 8 QN > / 0 (QN0 / 8 )
N
QN 0/ 8
BN 6 I` lckpcsmtmcb b”gst p`s i”íqumprcfgltmvmtí 6 igs vgltgurs lckpcs`btgs bg scbt p`s acrlíkgbt crtdcocb`ux. KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 07/01
4 scimjgs scbt gb kcuvgkgbt pi`b sur pi`b (jg pi`b (jg bcrk`ig z ), `icrs è tcut mbst`bt cb mbst`bt cb pgut lcbsmjírgr qug ig kcuvgkgbt jg >/0 cu 0/> gst ubg rct`tmcb `utcur j”ub `xg jg rct`tmcb jg rct`tmcb jg jmrgltmcb z . \m ig kcuvgkgbt gst qugilcbqug, lgt `xg jg rct`tmcb sg jípi`lgr` è jípi`lgr` è ld`qug mbst`bt pgrpgbjmlui`mrgkgbt `u pi`b j'ítujg 6 l”gst ub `xg mbst`bt`bí jg rct`tmcb. Xcur ub kcuvgkgbt jg rct`tmcb, lgt `xg gst amxg. Bctcbs M >/0 cu M 0/> ig pcmbt j”mbtgrsgltmcb gbtrg i”`xg mbst`bt`bí jg rct`tmcb gt ig pi`b jg i”ítujg. M >/0 gst `icrs `ppgií lgbtrg mbst`bt`bí jg rct`tmcb (LM^) ju kcuvgkgbt jg >/0.
Xrcprmítís ju LM^.
0) M>/0 M 0/ > lgbtrg mbst`bt`bí jg rct`tmcb
Q M >/0 8 (vmtgssg buiig buiig `u lgbtrg lgbtrg jg rct`t rct`tmcb) mcb) >/0
>) QX>/0 QM >/0>/0 XM>/0 pgrpgbj bjmlu mlui`m i`mrg rgss >/0 QX > / 0 XM >/0 >/0 Q X >/0 gt XM >/0 pgrpg /0 XM>/0 . >/0 .^ (l`r XM >/ 0 >/0 ) Q X >/0 gst prcpcrtmcbbgiig è XM >/0
^íp`rtmtmcb imbí`mrg jgs vgltgurs vmtgssgs. I` ríp`rtmtmcb jgs vgltgurs vmtgssgs jgs pcmbts jg \ p`r r`ppcrt è ^ gst sgkni`nig è lgiig jg tcut kcuvgkgbt jg rct`tmcb `utcur ju pcmbt M 6 imbí`rmtí jgs vmtgssgs vmtgssgs sur tcutg jrcmtg p` p`ss`bt ss`bt p`r ig LM^, ío`imtí jgs bcrkgs bcrkgs jgs vgltgurs vmtgssgs vmtgssgs pcur tcus igs pcmbts smtuís smtuís è i` kækg jmst`blg ju LM^.
I` sguig p`rtmlui`rmtí gst qug ig pcmbt M pgut ld`bo ld`bo gr jg pcs mtmcb mtmc b è tcut mb mbss t` t`bt. bt.
Jítgrkmb`tmcb oíckítrmqug ju LM^.
Mi gst prmkcrjm`i jg smtugr ig LM^, l`r s”mi gst lcbbu, mi pgrkgt jg jítgrkmbgr tcus igs vgltgurs vmtgssgs jgs pcmbts `pp`rtgb`bt è ub scimjg è p`rtmr jg i` jcbbíg j”ub sgui jg lgs vgltgurs vmtgssgs. 0/ Lcbb`mss`bt > vgltgurs vmtgssgs, ig LM^ sg pi`lg è i”mbtgrsgltmcb jgs bcrk`igs bcrk`igs è lgs > vgltgurs vmtgssgs. BN 6 J`bs ub kcuvgkgbt pi`b sur pi`b, tcutgs igs bcrk`igs `ux vmtgssgs scbt lcblcur`btgs `u LM^. >/ Xcur ub kcuvgkgbt jg rct`tmcb, ig LM^ gst amxg, l”gst ig lgbtrg jg rct`tmcb. 808
Lcurs 87 - Lmbík`tmqug ju scimjg mbjíacrk`nig
X`og 01/01
Zdícräkg jgs trcms pi`bs oimss`bts.
\cmt \0, \> gt \< trcms scimjgs gb kcuvgkgbt pi`b sur pi`b jg bcrk`ig z . Cb bctg M >/0 , M gt M /0, gt /0 > /0.z , < / > < / > .z gt < /0 < /0.z igs vgltgurs rct`tmcb `ssclmís.
X`r i` jíambmtmcb, bcus `vcbs 6
0 8 Q M >/ >/0 >/0 0>/
Gb `ppimqu`bt i` lckpcsmtmcb jgs vgltgurs vmtgssgs, cb `
/0M>/ < M>
> / /0M>/ < >/ < .z
Jcbl 6
QM < /0/0M>/ < >/ <
Xums i` icm ju ld`kp jgs vgltgurs vmtgssgs
QM >/0>>// <
M>/0M/< .M>/0M>>//< /0M /0M>>// < < /0.M> /0M /0M .M> /0M< 8
M < / > gt > / < < / > , cb `
M>/0< M /0 gt M>/ >/0 0M lcimbí`mrgs
Lcbliusmcb 6 Igs LM^ jgs kcuvgkgbts kcuvgkgbts rgi`tmas M >/0 , M gt M /0 < / > M>/0 / 8
Gxgkpig 6 I` prcprmítí j”`imobgkgbt j”`imobgkgbt jgs LM^ gst utmimsíg pcur jítgrkmbgr ig LM^ ju kcuvgkgbt jg >/8.
>
M> / 0
M< / >
0
<
M< / 8
M0/ 8 8
8
4 vgltgurs Q L 0/8 . 0/8 gt Q J
\ m cb lcbb`ât lcb b`ât 6 - 0 vgltgur Q L 0/8 ,
Cb gb jíjumt Q N 0/8 l`r 6 QN0/ 8 .NL QL 0/ 8 .NL
Gb > acms i”íqumprcfgltmvmtí, QN`ppimqu`bt 0/ 8 .NL QL 0/ 8 .NL gt QN0/ 8 .NJ QJ0/ 8 .NJ
cb lcbstrumt > prcfgltmcbs jg Q N 0/8 qug i”cb pgut jíjumrg.
( Q N 0/8 ` i` kækg prcfgltmcb sur (NL) qug Q L 0/8 ) Jmrgltmcb lcbbug
QL 0/ 8
N
jg QN 0/ 8
QL 0/ 8
QN 0/ 8
J
QJ 0/ 8
QN 0/ 8 N L
L
KX\M-XL\M
\lmgblgs Mbjustrmgiigs Mbjustrmgi igs pcur i”Mboíbmgur
\. Oíbcuåi
00/00/>808
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