CONTROL OF A SPACE ROBOT FOR CAPTURING A TUMBLING OBJECT
|
|
- Poppy Ray
- 6 years ago
- Views:
Transcription
1 CONROL OF A SPACE ROBO FOR CAPURING A UMBLING OBJEC Ou Ma (), Agl Flos-Abad (), Khah Pham (2) () Dpam o Mchacal ad Aospac Egg, Nw Mxco Sa Uvsy, Las Cucs, NM 88, USA Emal: oma@msu.du, a_abad@msu.du (2) U.S. A Foc Rsach Laboaoy, Spac Vhcl Dcoa, Klad A Foc Bas, NM , USA Emal: AFRL.RVSV@klad.a.ml ABSRAC hs pap pss a opmal cool sagy o a spac obo o capu a -umblg objc ud h codo o havg mmal mpac o h bas sall dug h capug opao. h da s o s pdc a ag m, locao ad spd o h umblg objc o h obo o cp wh such ha, wh h obo had physcally ouchs h objc, wll as a mmal agula mpuls o h bas sall. h, a opmal moo ajcoy ad h cospodg jo oqus wll b gad o cool h obo o ach h objc a h agd m ad locao. Jo a ad oqu lms wll b ak o accou h opmal cool soluo. Sc h cool acs bo a physcal coac happs, wll o ac ay xsg complac cool capably o h spac obo gadg boh mplmao ad opao. ho, h poposd mhod ca co-xs wh a xsg complac cool mhod h obo cool sysm. A umcal smulao xampl s psd o dmosa h cvss o h poposd mhod. A umcal smulao xampl s psd o dmosa h cvss o h poposd mhod.. GENERAL SPECIFICAIONS Spac mapulaos hav b succssully usd o may applcaos such as mauvg asoaus, bhg ad dployg lag spac sucus, cosucg ad maag h Iaoal Spac Sao (ISS), xplog ad sampl-collcg, sall o-ob svcg (chology dmos oly), c. All o hs mapulao acvs dal wh coopav payloads o ag objcs ad hus, h xsg obocs chologs ca hadl hm qu wll, hough may mpovms such as h opaoal ccy ad dxy may sll b do. Howv, a mapulao s xpcd o pom mo challgg ad sk asks, such as o capu a ukow objc, lk a pc o spac dbs, o a o-coopav objc, such as a umblg sall, h culy avalabl spac obocs chologs a sll a om bg ady. o mak hs challgg asks paccal, may ablg chologs hav o b uh advacd. hs sach dvlops ablg chology o a spac mapulao o capu a umblg sall. h opao o capug a umblg sall a complo o h dzvous pocss may b dvdd o ou phass. h s phas s h obsvg ad plag phas, whch s o acqu moo (maly oaoal moo) omao o h ag sall ad h dm wh ad wh o gasp h ag sall. h scod phas s h al appoachg phas, whch h obo s coolld o mov s dco o h plad gaspg locao o gaspg h ag sall a h plad m. h hd phas s h capug (o cpo) phas, whch h obo capus h ag sall. hs s h phas wh physcal coac happs ad hus s also h mos sky phas. h las s h pos-capu sablzao phas whch h umblg ag sall s dumbld ad sablzd by h obo ad svcg sall. h wok pod hs pap s cocd oly wh h plag pa o h s phas ad h whol scod phas. Ou ocus o h s phas s o dm a opmal m ad locao basd o h umblg moo o h ag sall o h obo s d-co o cp wh h ag sall. h ocus o h scod phas s o cool h obo o ach h opmal locao wh a mmal dsubac o h aud o h svcg sall o sa capu o h umblg ag sall. Rsach o h obsvao pa o h s phas has b do by may sachs h lds o compu vso ad ssg chologs. h hd ad ouh phass a mo sky ad challgg bcaus o h volvm o physcal coac. Som sach wok has b do bu much mo uu wok s absoluly qud od o hav guaad sa ad succssul uu mssos. W wll o dscuss hs h bcaus hy a ou o h scop o h pap. h mpac mmzao poblm o capug a ag objc has b sudd by a w sachs om d pspcvs. Yoshda al [] modld h collso dyamcs dug h capug pocss usg h xdd galzd so. hy ocusd o h moms jus bo ad a h mpac usg vlocy laos. Yoshda ad Nchv [2] oducd h cocp o aco ull-spac o aalyz h mpac ad pos-mpac moms o h capug pocss. hy oud ha choosg coguaos wh h aco
2 ull-spac o h svcg mapulao sysm ca sul a opao wh mmum mpac o h aud o h svcg sall. Papadopoulos ad Paaskvas [] poposd a mhodology basd o h pcusso po o bods o mmz h ocs sad o h momum asmd o h bas o h mapulao wh gaspg a objc. I all h pas suds h coac oc was jus a assumd mpulsv oc xd o h p o h mapulao whou akg o accou o h gomy o h coacg bods ad h umblg moo o h ag sall. I hs sach, w mov a sp owad o cosd h umblg moo o h ag sall h obo cool sagy o achvg mmal aud mpac o h svcg sall. h poblm o opmal ajcoy plag o a spac mapulao was addssd al by Duvowsky ad os [4]. hy oducd a hacd dsubac map, whch ca ad slcg a pah ha ducs h dsubacs o h bas spacca by dyg h dco o ach jo movm whch suls mmum o maxmum dsubacs. Agawal ad Xu [5] poposd a global opmum pah plag o duda spac mapulaos usg a vaaoal appoach o mmz h objcv ucoal wh cosas h la ad agula momum. Lampallo al [6] poposd a opmal moo plag mhod usg ca h jo spac. Huag al [7] poposd a opmal appoach ajcoy plag mhod o mmzg h mpac o h bas sall, h opmal ajcoy s oud basd o a gc algohm ad h dyamc couplg aco. Aghl [8] dsgd a opmal cooll o capu a umblg sall usg a objcv uco mmzg h opao m ad lav vlocy bw h obo p ad h ag.. Ok al [9] also poposd a opmal cool mhod o capu a umblg sall bu hy ocusd maly o mmzg h opaoal m o as capu. h ma dc bw ou appoach ad hos opmal cool appoachs s ha w ocus o h mmzao o h aco oqu o h svcg sall o sa capu opao. I hs pap, h ms svcg sall ad bas sall a xchagabl, so a h ms ag objc ad ag sall ad h ms mapulao ad obo. 2. DYNAMICS MODELLING 2.. Basc assumpos h dvlopm o h mhodology dscbd hs pap s basd o ollowg basc assumpos: (a) Boh h svcg sall ad h ag objc a assumd o b gd bods. h mapulao also cosss o gd lks. (b) h mass pops ad moo sa o boh h bas sall ad h ag objc a assumd kow. (c) h mauvs a clos poxmy ag ad hus h c o obal mchacs s glcd. (d) h aud o h bas sall s ully coolld ulss ohws sad. Assumpo (a) s a vy usual assumpo h obocs ld, spcally o dvlopm ad paccal mplmao o cool mhodologs bcaus a gd-body dyamcal sysm s much as o modl ad aalyz. I may applcaos such assumpo s also paccally suc. hs assumpo may b oo o aly o a log spac mapulao o capu a as umblg objc. Assumpo (b) s o ocus h sach o h obo cool poblm ad avod dalg wh h a dcao ad moo sa smao poblms, whch a wo sach aas havg b wll sudd ad a couously bg sudd by may oh sachs. Assumpo (c) s o ocus h sach o h scop o poxmy dzvous ad capu, wh h ocs/moms lad o obal mchacs a glgbl compad o h a ocs causd by h obo moo ad h coac ocs causd by h physcal cpo. Assumpo (d) has b a commo appoach o all h paccal capug opaos spac bcaus ucoolld aud ca sgcaly cas h possbly o msso alu. W a wll awa ha hs assumpos may o b alsc may applcao cass. hy a mposd o acla ou aly dvlopm o h chology. W wll b laxg hs assumpos h uu sach Dyamcs Modllg o h Svcg Sysm h mulbody sysm o h svcg sall ad h mapulao cosss o gd bods cocd by jos, as show Fg.. Body s h sall whch s also h bas o h obo ad body (,2,, ) s h -h lk o h mapulao. Jo has 6 dgs o dom whch cocs h a am o h svcg sall ad Jo ( j,2,, ) has oly o dg o dom whch aculas lks - ad. h symbols appag Fg. a dd as ollows: θ R : galzd jo coodas τ R : galzd jo oqus R : poso vco o h CM o Body R : poso vco o h mass c o h c svcg sysm R : poso vco o h mapulao d-co
3 a R :abodyvco o lk xpssd F am c R : poso vco o h CM o Lk masud om Jo z R : oaoal axs o h h jo v R : la vlocy o h mass c o Lk ω R : agula vlocy o h hlk v R : la vlocy o h svcg sall ω R : agula vlocy o h svcg sall v R : la vlocy o h d-co ω R : agula vlocy o h d-co R 6 : xal oc ad mom xd o h d-co 6 R : xal oc ad mom xd o h svcg sall R : aco ocs a h h oo o h mapulao τ R : aco oqu a h h oo o h mapulao z 2 2 Lk F2 ω a v C z τ F c Lk 2 a2 c2 ω 2 C2 a v 2 ω ω F- O- c oc c- C Lk - a- c C- F z v F c Lk a C Svc Sall Body (B ) v F ω ω Fg. Mulbody dyamc sysm o a svcg sall ad a spac mapulao I h al plag ad appoachg phass h a o xal ocs acg o h sysms ad hus, h momum o h svcg sysm wll b cosvd, om whch w ca dv h dyamcs quao o h spac obo ms o s jo vaabls θ as ollows []: wh Hθ Cθ τ () Cθ θ Hθ R θ 2 whch cluds h ola Cools ad cugal ocs acg o h sysm ad b b b R v (2) H H H H H () Moov, H s h galzd a max o h mapulao wh s aachd o a -loag bas. h oh vaabls o h sysm a dd as ollows: H J I J R : galzd a max o h mapulao as s aachd o a xd bas. 6 b m R : H J H couplg a max bw h svcg sall ad h mapulao. H b m mr mrc H svcg sall. c R 66 : a max o h I R :a max o lk wh spc o s mass c J z z2... z... R : Jacoba max o h agula vlocy o h -h body. J z ρ z ρ z ρ v c 2 c2 c R Jacoba max o h la vlocy o h -h body J mj m v R m v R H I J Z J m : oal mass o h svcg sysm m : mass o h -h body R : dy max z() z(2) Z z () z () R : max om o z(2) z() ps h coss poduc opao o ay vco. H I m RR I R ρcj R : poso vco om h jh jo o h mass c o h h body. 2.. Dyamcs Modllg o h ag Sall Sc h ag sall s assumd o b a sgl oag gd body, s dyamcs quao s ah smpl, Iω +ω Iω = τ (4) wh
4 I R : a max o h ag sall. ω R : agula vlocy o h ag sall. ω R : agula acclao o h ag sall. τ R : xal oqu appld o h ag sall. Basd o h assumpo o gog h obal mchacs, h xal oqu τ s zo bo a capu opao ad s h coac oqu dug capug.. DEERMINAION OF HE OPIMAL CAPURE IME As w hav sad aly, h ovall goal o h cool dsg s o capu h umblg sall wh mmal mpac o h aud moo o h svcg sall. h s sp o achvg such a goal s o dm a bs m o h obo o gasp. I s udsadabl ha h sula coac oc xd a h obo p (sulg om a capu aco) passs h mass c o h svcg sysm, h coac oc wll o caus ay aud dsubac o h svcg sall, as show Fg. 2. Howv, h dco o coac oc dpds o h lav vlocy, coacg spos ad coac gomy, whch mak vy dcul o pdc advac. Alhough such a pdco may o b mpossbl w hav a accua coac dyamcs modl, hs wll qu mo xsv sach wok h uu. Fo hs wok, w appoxma by assumg ha h coac oc s alog h dco o h lav vlocy bw h obo p ad h gaspg hadl o h ag sall. ho, o aud dsubac o h svcg sall ca b achvd by h o h ollowg codos: ) h lav vlocy bw h obo p ad h gaspg hadl o h ag sall s zo. 2) h lav vlocy s ozo bu s dco passs hough h mass c o h svcg sysm. h dsg o cool sags o m s codo s a commo appoach such as h wok dscbd [8]. I qus ha h obo p mus mov as as as h gaspg hadl o h umblg sall. hs s vy dcul o mpossbl wh h ag sall has a as umblg moo bcaus h p spd o a mapulao s always lmd o oly by h jo a lms bu also by h aud olac o h svcg sall. I such a cas, a sagy usg h scod codo as s cool goal bcoms mo aacv bcaus dos o qus zo lav vlocy, bu such a appoach has o b sudd h pas ho, w wll ocus ou sudy o achvg h scod codo. As show Fg., h scod codo mas ha h agl β (bw h lav vlocy ad h poso vco o h gaspg hadl o h ag sall) should b zo. I such a cas, h majo compo o h mpac oc (assumg maly alog h lav-vlocy dco) wll pass hough h mass c o h svcg sysm ad hus, caus o agula mom o h svcg sall. O cous, hs s oly a dal cas. I a gal umblg cas, h dco o h lav vlocy may v pass hough h mass c o h svcg sall. Howv, v h β agl ca v ach zo, wll always hav a mmal valu a a ca m. Hc, w wll jus ocus o h poblm o dm such a mmal agl. hs ca b omulad as: gv a s o al moo codos o h ag sall, d a uu m such ha h vlocy o h gaspg hadl, v ( ), wll hav zo o mmum momum abou h mass c o h svcg sysm. Mahmacally, hs ca b xpssd as wh v( ) ( ) max cos max v( ) ( ) v( ) v R( ωa) () Ra c Mass c o h svcg sysm (5) (6) Fg. 2 Icpo o mmal mpac o h bas sall basd o h coac oc dco. I h abov poblm do, R R s h oao max dg oao o h sall am F wh spc o h obal am F. Poso vco a pos o h gaspg hadl om h mass c o h ag sall, xpssd h sall s body-xd am F. No ha boh max R ad vco ω a ola ucos o m alhough h sall s udgog a oqu oao. R () ad ω () ca b solvd om h ollowg dyamcs quao ad kow al codos:
5 I ω + ω I ω = ()=, v() v, ω () ω (7) Soluo o ω () o ay gv m h sall local am ca b obad closd-om hough h valuao o Jacoba Ellpc ucos []. Howv, h closd-om soluo o ω () global am ad h closd-om soluo o h oao R() a vy dcul, as dscussd cly [4]. A ay a, umcal soluo o h opmzao poblm (5) s always possbl. Wh h a o xal ocs ad moms appld o h ag sall, s umblg moo should b podcal ov h m. hus, h abovdscussd opmal capu m wll b pad wh h pod o h sall s umblg moo. hs mas ha w ca hav ough m o ppa o a sa ad opmal capu bcaus h dsd capu m ad oppouy wll com padly ov h m. O cous, h aly, h ag wll ulkly b dog pcly podc oao bcaus h always xs som o-zo xal ocs ad moms as wll as dampg acos h sysm. ho, h umblg moo may o b kp h sam pod ov. Howv, such chagg s lkly b slow m ad hus, w wll sll hav m o pla ad pom a opmal capu ask, as dscbd h x sco. ω() ω R () R Gaspg hadl F z Mass c o svcg sysm h() h v() ω() Mass c o z ag sall () y y ω( ) ω? R( ) R v () v( ) F ( ) x ( )? Fg. Icpo o mmal mpac o h bas sall basd o h coac oc dco 4. OIMAL CONROL FOR HE ROBO S FINAL APPROACHING Oc a opmal m o capug s dmd, h cospodg moo sa o h ag sall ca also b calculad. hs opmal m ad moo sa wll b usd as h al m ad ag pos o h dco o dvlopg h cool o h obo o pom h capu ask. o ocus o h obocs cool, s assumd ha h svcg sall has z y F x ( ) a v ω( ) b coolld o kp a xd dsac o h ag sall such ha h ag sall s wh h ach o h oboc am. o dvlop h opmal cool, h obo s dyamcs quao () s w o a sa spac om as ollows x (x) G(x)τ (8) 2 2 wh x R s h sa vco; R s h sa 2 uco, G R s h cool max; ad τ R s h jo cool oqus. hy a dd as x θ x x2 θ x (x) (9) H(x ) C(x) x2 G(x) H(x ) Assumg ha h svcg sall s ully coolld, w ca d h mpac o h obo moo o h svcg sall by dvg h aco oc ad mom τ (s Fg. ) o h oo o h obo (a h s obo jo), amly, c τ τc ( a ) c () mv ( x, x) (, ) c ( ) m τ x x I ω a v wh c R ad τ c R a h a oc ad mom acg a h mass c o h h body, spcvly; R ad τ R a h oal oc ad mom h obo appls a h s oo, spcvly. ho, h oal aco oc ad mom causd by h obo moo a h mass c o h svcg sall a τ c τc c m v ( x, x) (, ) c m τ x x I ω Rv () Ou cool goal s h o d a m hsoy o ach jo s cool oqu such ha, wh h mapulao s p s coolld by hs s o jo oqus o mov om s al pos o s al pos,
6 wll hav mmal aud dsubac o h svcg sall. o d hs s o opmal cool oqus, w ca us h ollowg objcv uco θ θ J τ τd, x() x, x( ) x (2) θ θ Fo hs opmal cool poblm, h al sa x s kow ad h al m ad al sa x( ) a dmd by solvg h cosad opmzao poblm dd sco. h Maxmum pcpl [2] lls us ha a cssay codo o a opmal cool τ () s o maxmz h ollowg Poyag Hamloa H H( x, λ, τ) τ τ λ ( Gτ ) () 2 wh λ R s h vco o cosa vaabls. h, h cssay codos o h soluo ca b w h ollowg om λ H H, x (4) x λ wh h al ad al codos gv (2). Fo ou poblm, h al m ad al moo sa o h opmal cool a kow. I oh wods, s a xd m ad xd bouday poblm. Howv, bcaus o s complx ola au, sll has o b solvd umcally. 5. SIMULAION EXAMPLE o show h applcao o h ao-mod opmal cool sagy, w ps a xampl usg a 2-DOF plaa mapulao hs sco. h paams o h salls ad obo a dd Fg. 4 ad abl. Rlav vlocy pog o h svcg sall s COM c.5m Fully Coolld Bas Sall c 2 v() v( ) Mass c o h svcg sall sysm 4 ω ω Gaspg hadl Ed-co ajcoy wh mmu aco oqu Fg. 4 Exampl o 2-DOF spac mapulao appoachg a squa ag o capug abl. Paams o h 2-DOF spac mapulao Body Body o. (m) c (m) m (Kg) I (Kg m 2 ) Bas sall Robo lk Robo lk ag sall Dmao o h opmal m ad sa h sysm s assumd as show Fg. 4, h c o mass o h svcg sysm cludg h obo ca b oud o b: C m W also assum ha : m 2 a.5 m s.2.4 m R(), () [2.7.4 ] m, ω =.47 ad/sc, v().75 m/s I h 2-D cas, h oaoal moo s smpl ad hus, w ca asly d ha h opmal m ad oao o h ag sall o h obo o capu wh zo aud mpac a 4s v( ) R( ω a ) [ ] m/s R ( ) Opmal Cooll o h Fal Appoachg Followg h mhod oducd Sco 5, h opmal cool o h obo s dd as ollows: subjc o: 4sc dx d τ τ Mmz J d J( x,τ ) dx2 dx dx4 x ; x 4 ; x ad x 4, d d d ( ) [2 ] ; x ( ) [ ] ( ) [.47.2 ] ; x ( ) [.5.5 ] h opmal cool poblm was solvd umcally usg h omlab sowa. Fgu 5 shows h mapulao s jo dsplacms. Fg. 6 shows h appld jo oqus dvg h obo om s al
7 Raco mom (Nm) Jo oqus (Nm) Jo agls (ad) Raco mom (Nm) Jo agls (ad) coguao o h ag coguao o capug h ag sall. I ca b ocd ha boh jos ach h dsd al posos a h dsd m. I s 4sg o s ha h scod lk movs a lo (owad s ad h backwad). hs s cssay o h pupos o achvg h goal o havg a mmum accumulad aco mom o h bas sall dug h am mauvg. Fg. 7 claly dcas ha h aco oqu a h aco oqu o h svcg sall s vy small ( h lvl o mco Nwos). ho, w ca coclud ha h dsd opmal cool goal has b achvd cool. As a sul, such a obo mauv wll hav a sgca sk o dsablzg h bas sall m (sc) 2 Fg. 8 Jo ajcos o h obo om h soluo o a o-opmal cool m (sc) Fg. 5 Jo ajcos o h obo om h soluo o h opmal cool m (sc) Fg. 6 Jo cool oqus om h soluo o h opmal cool x m (s) Fg. 7 Raco oqu o h bas sall I od o s h advaag o h poposd opmal cool, w also mplmd a usual obo cooll o achvg h sam p moo ag wh h sam m lm. h sulg jo ajcos o such a oopmal cool a show Fg. 8. Obvously, h bhavo o h jo moo, as show Fg. 8, sms b ha ha om h opmal cool show Fg. 5. Howv, h aco oqu hs cas, as dpcd Fg. 9, s much lag ha ha om h opmal 2 x y z m (sc) Fg. 9 Jo cool oqus om h soluo o a o-opmal cool 6. CONCLUSIONS A opmal cool sagy o a spac mapulao o capu a umblg sall was psd. h goal o h cool sagy s o mmz h mpac o h aud o h svcg sall. hs s do wo sps: ) d a opmal m ad h cospodg moo sa o h umblg sall such ha h physcal cpo om capug opao wll hav zo o mmal aud mpac o h svcg sall; 2) cool h obo p o ach h umblg sall a h opmal m ad also caus mmal aco mom o h svcg sall dug h moo o h obo. hs appoach s maly amd a sa opao o capug a as umblg sall, whch s ohws a vy dcul ad sky opao. A 2D xampl was psd o dmosa h applcao o h poposd mhod. h xampl shows ha, wh h opmal cool, h oaoal dsubac o h bas sall s almos zo whl h ag ca sll b achd a h opmal m. Culy, w a sudyg h sags ad pomac o h cass wh h s sp us a sul havg adom os (.., h smad opmal capu m ad sa hav ucas). Fuh, h sudy o h pomac o h poposd chology o gal 6- DOF mapulaos cludg capug coac dyamcs s also h plad uu wok o h hs sach pojc. x y z
8 7. KNOWLADGMENS hs maal s basd o h sach wok sposod by h US A Foc Rsach Laboaoy (AFRL) ud agm umb FA h U.S. Govm s auhozd o poduc ad dsbu ps o Govmal puposs owhsadg ay copygh oao ho. h vws ad coclusos coad h a hos o h auhos ad should o b pd as cssaly psg h ocal polcs o dosms, h xpssd o mpld, o A Foc Rsach Laboaoy o h US Govm. 8. REFERENCES. Yoshda, K., Kuazum, R., Sashda, N., Uma, Y., (992). Modlg o Collso Dyamcs o Spac F-Floag lks wh h Exdd Galzd Ia so. IEEE Iaoal Coc o Robocs ad Auomao, Nc, Fac, pp Yoshda, K., ad Nchv, D. N. (995). Spac Robo Impac Aalyss ad Sall-Bas Impuls Mmzao Usg Raco Null-Spac. IEEE Iaoal Coc o Robocs ad Auomao, Nagoya, Japa, pp Papadopoulos, E. ad Paaskvas, I. (25). Dsg ad Coguao Cool o Spac Robos Udgog Impacs. 6h Iaoal ESA Coc o Gudac, Navgao ad Cool Sysms, Louak, Gc, pp Dubowsky, S., ad os, M. (99). Pah Plag o Spac Mapulaos o Mmz Spacca Aud Dsubacs. IEEE Iaoal Coc o Robocs ad Auomao, Sacamo, CA., pp Agawal, O. P. ad Xu, Y. (994). O h global opmum pah plag o duda spac mapulaos. IEEE asacos o Ma ad Cybcs. 24(9) Lampallo, R., Agawal, S., ad Hzg, H. (2). Opmal Moo Plag o F-Flyg Robos, IEEE Iaoal Coc o Robocs ad Auomao, ap, awa, pp Huag, P., Yua, J., Xu, Y., ad Lu, R. (26). Appoach ajcoy Plag o Spac Robo o Impac Mmzao. IEEE Iaoal Coc o Iomao ad Acquso, Shadog, Cha, pp Aghl. F. (28). Opmal Cool o Roboc Capug ad Passvao o a umblg Sall wh Ukow Dyamcs. AIAA Gudac Navgao ad Cool Coc, Hoolulu, Hawa, pp Ok,. Nakash, H ad Yoshda, K. (28). m- Opmal Mapulao Cool o a F-Floag Spac Robo wh Cosa o Raco oqu. IEEE Iaoal Coc o Illg Robos ad Sysms, Nc, Fac, pp Xu, Y., ad Kaad,., Eds. (99). Spac obocs: Dyamcs ad Cool. Kluw Acadmc Publshs.. Yoshda, K., ad Nchv, D. N. (999). Impac Aalyss ad Pos-Impac Moo Cool Issus o a F-Floag Spac Robo Subjc o a Foc Impuls. IEEE asacos o Robocs ad Auomao, 5(), Poyag, L.S., Bolyask, V.G., Gamkldz, R.V., Ad Mshchko, E.F. (964). h Mahmacal hoy o Opmal Pocsss (aslad by D. E. Bow), Macmlla Compay.. Jupp, A. H. (974). O h oao o a gd body. Clsal Mchacs, 9(), Zo, R.V. ad Schold, J. (27). Numcal mplmao o h xac dyamcs o gd bods. Joual o Compuaoal Physcs. 25 (),
k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)
TOTAL INTRNAL RFLTION Kmacs pops Sc h vcos a coplaa, l s cosd h cd pla cocds wh h X pla; hc 0. y y y osd h cas whch h lgh s cd fom h mdum of hgh dx of faco >. Fo cd agls ga ha h ccal agl s 1 ( /, h hooal
More informationAnouncements. Conjugate Gradients. Steepest Descent. Outline. Steepest Descent. Steepest Descent
oucms Couga Gas Mchal Kazha (6.657) Ifomao abou h Sma (6.757) hav b pos ol: hp://www.cs.hu.u/~msha Tch Spcs: o M o Tusay afoo. o Two paps scuss ach w. o Vos fo w s caa paps u by Thusay vg. Oul Rvw of Sps
More informationPhys Nov. 3, 2017 Today s Topics. Continue Chapter 2: Electromagnetic Theory, Photons, and Light Reading for Next Time
Phys 31. No. 3, 17 Today s Topcs Cou Chap : lcomagc Thoy, Phoos, ad Lgh Radg fo Nx Tm 1 By Wdsday: Radg hs Wk Fsh Fowls Ch. (.3.11 Polazao Thoy, Jos Macs, Fsl uaos ad Bws s Agl Homwok hs Wk Chap Homwok
More informationLecture Y4: Computational Optics I
Phooc ad opolcoc chologs DPMS: Advacd Maals Udsadg lgh ma acos s cucal fo w applcaos Lcu Y4: Compuaoal Opcs I lfos Ldoks Room Π, 65 746 ldok@cc.uo.g hp://cmsl.maals.uo.g/ldoks Rflco ad faco Toal al flco
More informationInternational Journal of Pure and Applied Sciences and Technology
I J Pu Appl Sc Tchol 8 pp 59-7 Iaoal Joual o Pu ad Appld Sccs ad Tchology ISSN 9-67 Avalabl ol a wwwopaasa Rsach Pap Tasmud Quas Ldly Dsbuo: A Galzao o h Quas Ldly Dsbuo I Elbaal ad M Elgahy * Isu o Sascal
More informationBoyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues
BocDPm 9 h d Ch 7.6: Compl Egvlus Elm Dffl Equos d Boud Vlu Poblms 9 h do b Wllm E. Boc d Rchd C. DPm 9 b Joh Wl & Sos Ic. W cosd g homogous ssm of fs od l quos wh cos l coffcs d hus h ssm c b w s ' A
More informationSOME IMPUTATION METHODS IN DOUBLE SAMPLING SCHEME FOR ESTIMATION OF POPULATION MEAN
aoal Joual of Mod Egg Rsach (JMER) www.jm.com ol. ssu. Ja-F 0 pp-00-07 N: 9- OME MPUTATON METHOD N DOUBLE AMPLNG HEME FOR ETMATON OF POPULATON MEAN ABTRAT Nada gh Thaku Kalpaa adav fo Mahmacal ccs (M)
More informationExistence of Nonoscillatory Solutions for a Class of N-order Neutral Differential Systems
Vo 3 No Mod Appd Scc Exsc of Nooscaoy Souos fo a Cass of N-od Nua Dffa Sysms Zhb Ch & Apg Zhag Dpam of Ifomao Egg Hua Uvsy of Tchoogy Hua 4 Cha E-ma: chzhbb@63com Th sach s facd by Hua Povc aua sccs fud
More informationLinear Perturbation Bounds of the Continuous-Time LMI-Based H Quadratic Stability Problem for Descriptor Systems
UGRN DE OF ENE ERNE ND NFORON EHNOOGE Volu No 4 ofa a ubao ouds of h ouous- -asd H uadac ably obl fo Dscpo yss dy ochv chcal Uvsy of ofa Faculy of uoacs Dpa of yss ad ool 756 ofa Eal ayochv@u-sofa.bg bsac
More informationPart I- Wave Reflection and Transmission at Normal Incident. Part II- Wave Reflection and Transmission at Oblique Incident
Apl 6, 3 Uboudd Mda Gudd Mda Chap 7 Chap 8 3 mls 3 o 3 M F bad Lgh wavs md by h su Pa I- Wav Rlo ad Tasmsso a Nomal Id Pa II- Wav Rlo ad Tasmsso a Oblqu Id Pa III- Gal Rlao Bw ad Wavguds ad Cavy Rsoao
More informationConvergence tests for the cluster DFT calculations
Covgc ss o h clus DF clculos. Covgc wh spc o bss s. s clculos o bss s covgc hv b po usg h PBE ucol o 7 os gg h-b. A s o h Guss bss ss wh csg s usss hs b us clug h -G -G** - ++G(p). A l sc o. Å h c bw h
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
W a cop wold s ladg pbls o Op Accss books Bl b scss o scss 8 6 M Op accss books avalabl aoal aos ad dos owloads O aos a amog 54 os dlvd o OP % mos cd scss.% obos om op 5 vss Slco o o books dd Book ao d
More informationCHAPTER: 3 INVERSE EXPONENTIAL DISTRIBUTION: DIFFERENT METHOD OF ESTIMATIONS
CHAPTER: 3 INVERSE EXPONENTIAL DISTRIBUTION: DIFFERENT METHOD OF ESTIMATIONS 3. INTRODUCTION Th Ivrs Expoal dsrbuo was roducd by Kllr ad Kamah (98) ad has b sudd ad dscussd as a lfm modl. If a radom varabl
More information8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system
8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.
More informationBy Joonghoe Dho. The irradiance at P is given by
CH. 9 c CH. 9 c By Joogo Do 9 Gal Coao 9. Gal Coao L co wo po ouc, S & S, mg moocomac wav o am qucy. L paao a b muc ga a. Loca am qucy. L paao a b muc ga a. Loca po obvao P a oug away om ouc o a a P wavo
More informationAssessing Student Work MATH RUBRIC. Understanding Reasoning Accuracy Communication
Assssg Sud Wk MATH RUBRIC E x 4 P a 3 A 2 N v 1 Udsadg Rasg Auay Cmmua Uss wful ad hugh Th dus a sags ladg dly gazd hughu ad ffv slus. asly fllwd by hs. Exls, aalyzs, ad All fas ad alulas jusfs all lams
More informationA Proportional Differentiation Model Based on Service Level
ppl. ah. If. c. 6 o. pp. 453-46 ppld ahmacs & Ifomao ccs Iaoal Joual @ aual ccs ublshg Co. opooal Dffao odl d o vc Lvl K-o Cho Dpam of Idusal & aagm gg Hau Uvsy of og uds Yog 449-79 Koa Cospodg auho: mal:
More informationStudy of Tyre Damping Ratio and In-Plane Time Domain Simulation with Modal Parameter Tyre Model (MPTM)
Sudy o Ty Damping aio and In-Plan Tim Domain Simulaion wih Modal Paam Ty Modl (MPTM D. Jin Shang, D. Baojang Li, and Po. Dihua Guan Sa Ky Laboaoy o Auomoiv Say and Engy, Tsinghua Univsiy, Bijing, China
More informationLecture 12: Introduction to nonlinear optics II.
Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal
More informationCharacterizing Optical Thin Films (I)
Chaaczg Opcal Th Flms (I) Physcal vapo dposo s h mos commo chqu usd o dpos opcal h lms o a lag vay o applcaos. Ths qus h ably o g a sold maal o a vapo (gasous) om, o aspo o a suac oo whch h lm s o b dposd,
More informationControl Systems (Lecture note #6)
6.5 Corol Sysms (Lcur o #6 Las Tm: Lar algbra rw Lar algbrac quaos soluos Paramrzao of all soluos Smlary rasformao: compao form Egalus ad gcors dagoal form bg pcur: o brach of h cours Vcor spacs marcs
More informationThe far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109
Th fa fl calculao: Appoa a ac oluo Pa K Novb 0h 005 B-09 Oul Novb 0h 005 Pa K Iouco Appoa oluo flco fo h gou ac oluo Cocluo Pla wav fo Ic fl: pla wav k ( ) jk H ( ) λ λ ( ) Polaao fo η 0 0 Hooal polaao
More informationGet Funky this Christmas Season with the Crew from Chunky Custard
Hol Gd Chcllo Adld o Hdly Fdy d Sudy Nhs Novb Dcb 2010 7p 11.30p G Fuky hs Chss Sso wh h Cw fo Chuky Cusd Fdy Nhs $99pp Sudy Nhs $115pp Tck pc cluds: Full Chss d buff, 4.5 hou bv pck, o sop. Ts & Codos
More informationChap 2: Reliability and Availability Models
Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h
More informationConvolution of Generated Random Variable from. Exponential Distribution with Stabilizer Constant
Appld Mamacal Scc Vol 9 5 o 9 78-789 HIKARI Ld wwwm-acom p://dxdoog/988/am5559 Covoluo of Gad Radom Vaabl fom Expoal Dbuo w Sablz Coa Dod Dvao Maa Lufaa Oaa ad Maa Aa Dpam of Mamac Facul of Mamac ad Naual
More informationHandout on. Crystal Symmetries and Energy Bands
dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h
More informationTrefftz method in solving the inverse problems
IP-A Ivs Poblms: vlopms ho a applcaos Fbua 9- Wasaw Pola ff mho solvg h vs poblms Ksof Gsa Klc Uvs of cholog Al.. -lca P.P.7 5-34 Klc Pola -mal: sof@gsa.pl /7 IP-A Ivs Poblms: vlopms ho a applcaos Fbua
More informationAlmost unbiased exponential estimator for the finite population mean
Almos ubasd poal smaor for f populao ma Rajs Sg, Pakaj aua, ad rmala Saa, Scool of Sascs, DAVV, Idor (M.P., Ida (rsgsa@aoo.com Flor Smaradac ar of Dparm of Mamacs, Uvrs of Mco, Gallup, USA (smarad@um.du
More informationAn Analysis of a Double-layer Electromagnetic Shield for a Universal Contactless Battery Charging Platform
A Aalyss of a Doubl-lay Elcomagc Shld fo a Uvsal Coaclss Bay Chagg Plafom Absac A pad doubl-lay plaa sucu s mployd o shld h lcomagc EM fld a h boom of a uvsal chagg plafom. Th doubl-lay cosss of a lay
More informationOption Pricing in a Fractional Brownian Motion Environment
Opo Pcg a acoal owa Moo vom Cpa Ncula Acamy o coomc u ucha, omaa mal: cpc@yahoo.com h a: buay, Abac h pupo o h pap o oba a acoal lack-chol omula o h pc o a opo o vy [, ], a acoal lack-chol quao a a k-ual
More informationStatics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r.
Statcs Th cotact btw a mapulato ad ts vomt sults tactv ocs ad momts at th mapulato/vomt tac. Statcs ams at aalyzg th latoshp btw th actuato dv tous ad th sultat oc ad momt appld at th mapulato dpot wh
More informationWARRANT VALUATION METHODS
ARRA ALUAIO MEHOD o R. aa Ph.D. FRM Mogom Ivsm cholog Ic. Fal am J 83 Pho: 6 688-8 so.saa@fools.com www.fools.com cos h cas of a Euopa sl waa ha ls h coac hol o bu a h sk pc o sha of h ulg sock. BLAK-HOLE-MERO
More informationAnalytical Evaluation of Multicenter Nuclear Attraction Integrals for Slater-Type Orbitals Using Guseinov Rotation-Angular Function
I. J. Cop. Mh. S Vo. 5 o. 7 39-3 Ay Evuo of Mu u Ao Ig fo S-yp O Ug Guov Roo-Agu uo Rz Y M Ag Dp of Mh uy of uo fo g A-Khj Uvy Kgo of Su A Dp of Mh uy of S o B Auh Uvy Kgo of Su A A. Ug h Guov oo-gu fuo
More information(ΔM s ) > (Δ M D ) PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING INFLATION ARBITRAGE AND THE LAW OF ONE PRICE
PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING Fv Pay Condons Rsul Fom Abag Acvs 1. Pucasng Pow Pay (PPP). T Fs Ec (FE) 3. T Innaonal Fs Ec (IFE) 4. Ins Ra Pay (IRP) 5. Unbasd Fowad
More informationBayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data
Bys Eso of h s of h Wull-Wull gh-bs xu suos usg so S. A. Sh N Bouss I.S.S. Co Uvsy I.N.P.S. Algs Uvsy shsh@yhoo.o ou005@yhoo.o As I hs h s of h Wull-Wull lgh s xu suos s usg h Gs slg hqu u y I sog sh.
More informationELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION
. l & a s s Vo Flds o as l axwll a l sla () l Fld () l olasao () a Flx s () a Fld () a do () ad è s ( ). F wo Sala Flds s b dd l a s ( ) ad oool a s ( ) a oal o 4 qaos 3 aabls - w o Lal osas - oz abo Lal-Sd
More informationCHAPTER 7. X and 2 = X
CHATR 7 Sco 7-7-. d r usd smors o. Th vrcs r d ; comr h S vrc hs cs / / S S Θ Θ Sc oh smors r usd mo o h vrcs would coclud h s h r smor wh h smllr vrc. 7-. [ ] Θ 7 7 7 7 7 7 [ ] Θ ] [ 7 6 Boh d r usd sms
More informationMECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals
MECE 330 MECE 330 Masurms & Isrumao Sac ad Damc Characrscs of Sgals Dr. Isaac Chouapall Dparm of Mchacal Egrg Uvrs of Txas Pa Amrca MECE 330 Sgal Cocps A sgal s h phscal formao abou a masurd varabl bg
More informationBayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP
By Cly o c o Lo Rc Rg By M Coco L Cl & Pcoc LLP GIRO coc 4 Ac Th pp c how o v cly wgh w po- pc-v o c o lo c. Th po co o Poo-Po ol ch wh po G o. Kywo c o lo c g By cly Poo Po G po Acowlg cl I wol l o h
More informationMean Estimation with Imputation in Two- Phase Sampling
Iaoal Joual of o gg sac (IJ) www.jm.com ol. Issu.5 p-oc. 0 pp-56-5 I: 4-6645 a smao w Impuao wo- Pas amplg aa g au Kalpaa aav aa Paa * fo amacal ccs () aasal Uvsaasal ajasa * pam of amacs a ascs. H.. Gou
More informationLeast squares and motion. Nuno Vasconcelos ECE Department, UCSD
Las squars ad moo uo Vascoclos ECE Dparm UCSD Pla for oda oda w wll dscuss moo smao hs s rsg wo was moo s vr usful as a cu for rcogo sgmao comprsso c. s a gra ampl of las squars problm w wll also wrap
More informationMathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem
Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao
More informationNumerical Solution of Transient Thermal Stresses in a Functionally Graded Cylinder
La d gg Mha gg Glgy al l f a hal a Fally Gadd yld IQ H KHOLO I-LMH aal gg a Jda y f ad hlgy P.O x Ibd JO al: daabh@.d. ba: - h a d h a hal a la yld ad f a fally gadd aal FGM. h yld aal dd b gadd alg h
More information2016 FALL PARKS DIVISION AND WATER UTILITY LANDSCAPING
- - - - - - - - - - - - - - - - - DU F O K CD G K CUC G K D K FD K GY GOF COU O K G O K GD O K KGO-OYX K O CK K G K COD K K K (KG O) UY O G CK KY UY F D UY CY OF DO D OF UC OK U O: --; --; --; --; ---
More informationPressure Transient Analysis for Non-Newtonian Power-Law Fluid Flow in Double Porous Media and Fractal Reservoirs
ssu Tas Aalyss o No-Noa o-la Flu Flo oubl oous Ma a Facal Rsvos HOU Yg M TONG g K ollg o Mahacs a opuaoal Sccha Uvsy o olu ogyg 576 houyg@upc.u.c Absac Ths pap pss a ahacal ol o as lo o h o-noa po-la lu
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationPhase plane method is an important graphical methods to deal with problems related to a second-order autonomous system.
NCTU Dpam of Elcical ad Compu Egiig Sio Cous
More informationExample: Two Stochastic Process u~u[0,1]
Co o Slo o Coco S Sh EE I Gholo h@h. ll Sochc Slo Dc Slo l h PLL c Mo o coco w h o c o Ic o Co B P o Go E A o o Po o Th h h o q o ol o oc o lco q ccc lco l Bc El: Uo Dbo Ucol Sl Ab bo col l G col G col
More informationRAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels
AKE v wh Apv f Cs fo DS-CDMA Ss Muph Fg Chs JooHu Y Su M EEE JHog M EEE Shoo of E Egg Sou o Uvs Sh-og Gw-gu Sou 5-74 Ko E-: ohu@su As hs pp pv AKE v wh vs og s popos fo DS-CDMA ss uph fg hs h popos pv
More informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More information(7) CALAMINTHA NEPETA 'WHITE CLOUD' (15) RUDBECKIA FULGIDA VAR.SULLIVANTII 'GOLDSTURM' (2) SPIRAEA JAPONICA 'ANTHONY WATERER'
XD DC D D ; () C ' COUD' () UDCK FUGD VUV 'GODU' () JOC 'OY ' () CGO X CUFO 'K FO' C f d Dpm f ub K DVO C-Cu ud, u u K, J vd O x d, - OV DG D VC Gp f CO OJC: F K DVO D UY DCG CUO XG CC COCO QUD O DGD U
More informationReliability analysis of time - dependent stress - strength system when the number of cycles follows binomial distribution
raoal Joural of Sascs ad Ssms SSN 97-675 Volum, Numbr 7,. 575-58 sarch da Publcaos h://www.rublcao.com labl aalss of m - dd srss - srgh ssm wh h umbr of ccls follows bomal dsrbuo T.Sumah Umamahswar, N.Swah,
More informationSeries of New Information Divergences, Properties and Corresponding Series of Metric Spaces
Srs of Nw Iforao Dvrgcs, Proprs ad Corrspodg Srs of Mrc Spacs K.C.Ja, Praphull Chhabra Profssor, Dpar of Mahacs, Malavya Naoal Isu of Tchology, Japur (Rajasha), Ida Ph.d Scholar, Dpar of Mahacs, Malavya
More informationNeutrosophic Hyperideals of Semihyperrings
Nuooph m Vol. 06 05 Uv o Nw Mo Nuooph Hpl o mhpg D Ml Dpm o Mhm j P Moh Collg Up Hooghl-758 mljumh@gml.om A. h pp w hv ou uooph hpl o mhpg o om opo o hm o u oo pop. Kwo: C Pou Compoo l o Nuooph mhpmg.
More informationGeometrical optics. Textbook: Born and Wolf (chapters 3-5) Overview:
Gomal ops Txbook: Bo a Wol aps -5 Ovvw: Elomag pla wavs om maxwll's quaos. T Ekoal quao a s vao ops a o wavlg. Rao ll's law lo Toal al lo T psm Dspso T ls Imagg as a pojv asomao. Opal ssms a ABCD max.
More informationCh. 22: Classical Theory of Harmonic Crystal
C. : Clssl Toy o mo Cysl gl o ml moo o o os l s ld o ls o pl ollowg:. Eqlbm Pops p o ls d Islos Eqlbm sy d Cos Egs Tml Epso d lg. Tspo Pops T pd o lo Tm Fl o Wdm-Fz Lw pody Tml Cody o Islos Tsmsso o od.
More informationMotion Control Systems Chapter 1
Asf Šboć Kouh Ohsh Moo Cool Syss Chp Elcochcl Syss Dycs Moo Cool Syss Asf Šboć Kouh Ohsh 0 oh Wly Sos (As) P Bsc us Mchcl Syss Poso locy Foc wok Mou x F F ( xx ) p p x x W F Fx x x Kc gy Pol gy ol gy xx
More informationCONTENTS. Hugo Reitzel, the pickles enthusiast CERTIFICATIONS JARS POUCHES & CANS SALAD DRESSING MINI-TUBES
v4. APRIL 2018. Hugo Rz, h pk hu Th of h uhd gu g ou Hugo Rz. I 1909, Ag, Sw vg, h uhd h ow op wh vo: o p up h wod of od! Ad fo ov o hudd ow, w hoo h hg b ug ou xp o o ov ou bu od o bo THE od p. W ufu
More informationGNSS-Based Orbit Determination for Highly Elliptical Orbit Satellites
-Bd D f Hghy p Q,*, ug, Ch Rz d Jy u Cg f u gg, g Uvy f u d u, Ch :6--987, -:.q@ud.uw.du. h f uvyg d p If y, Uvy f w uh W, u : h Hghy p H ufu f y/yhu f h dgd hv w ud pg h d hgh ud pg h f f h f. Du h g
More informationSTANLEV M. MOORE SLAIN IN COLORADO
MU O O BUDG Y j M O B G 3 O O O j> D M \ ) OD G D OM MY MO- - >j / \ M B «B O D M M (> M B M M B 2 B 2 M M : M M j M - ~ G B M M M M M M - - M B 93 92 G D B ; z M -; M M - - O M // D M B z - D M D - G
More informationEMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions
EMA5 Lecue 3 Seady Sae & Noseady Sae ffuso - Fck s d Law & Soluos EMA 5 Physcal Popees of Maeals Zhe heg (6) 3 Noseady Sae ff Fck s d Law Seady-Sae ffuso Seady Sae Seady Sae = Equlbum? No! Smlay: Sae fuco
More informationCrowds of eager worshippers trooping into the venue
LvWld Cv A lld y F uv Fdy m Juy ldg wk Fbuy, ud l gd LvWld Cv A Lg, Ng, l lg mg w P C ggd, Am F Ml Lv. Hly G-dzvu w Ld' y my. Adg P C, dd' ll mg. Ld lly lld m...h d l; w H wd. Cwd g w g vu AN APPNMEN WH
More informationDirect current regimes in the linear electric circuits according to the relativistic circuit theory
ISSN: 63-316X (Ol OI: 1.9114/av.vol.ss1.66 Vol Iss 1 (18 Pblshd: 18-6-3 c c gms h la lcc ccs accodg o h lavsc cc ho ml Ivaov Paov 1 1 Tchcal Uvs of Vaa, pam of Thocal lccal gg ad Ismao, 91, 1 Sdsa S, Vaa,
More informationGUIDE FOR SUPERVISORS 1. This event runs most efficiently with two to four extra volunteers to help proctor students and grade the student
GUIDE FOR SUPERVISORS 1. This vn uns mos fficinly wih wo o fou xa voluns o hlp poco sudns and gad h sudn scoshs. 2. EVENT PARAMETERS: Th vn supviso will povid scoshs. You will nd o bing a im, pns and pncils
More informationNLO Basics. Bulk Second Harmonic Generation Examples. QuartzQ ZnO bulk and nanowires Organic nanowires
NLO Bascs Bul Scod Hamoc Gao xampls QuaQ ZO bul ad aows Ogac aows Ahamoc Poals U U- P χ χ χ Io P lco pah P Wav quao : quaos Maxwlls D J H B : chags f No 4 H B J D B μ ρ ρ s. : chags f No H H B J μ μ ρ
More informationInternational Journal of Scientific & Engineering Research, Volume 7, Issue 5, May-2016 ISSN The Maximum Eccentricity Energy of a Graph
Iaoa Joa of cfc & Egg Rsach Vom 7 Iss 5 ay6 IN 955 5 Th axmm Ecccy Egy of a Gaph Ahmd Na ad N D o Absac I Ths pap w odc h cocp of a maxmm cccy max oba som coffcs of h chaacsc poyoma of a cocd gaph G ad
More informationAlmost Unbiased Exponential Estimator for the Finite Population Mean
Rajs Sg, Pakaj aua, rmala Saa Scool of Sascs, DAVV, Idor (M.P., Ida Flor Smaradac Uvrs of Mco, USA Almos Ubasd Epoal Esmaor for F Populao Ma Publsd : Rajs Sg, Pakaj aua, rmala Saa, Flor Smaradac (Edors
More information11/8/2002 CS 258 HW 2
/8/ CS 58 HW. G o a a qc of aa h < fo a I o goa o co a C cc c F ch ha F fo a I A If cc - c a co h aoa coo o ho o choo h o qc? I o g o -coa o o-coa? W ca choo h o qc o h a a h aa a. Tha f o o a h o h a:.
More informationFor the plane motion of a rigid body, an additional equation is needed to specify the state of rotation of the body.
The kecs of rgd bodes reas he relaoshps bewee he exeral forces acg o a body ad he correspodg raslaoal ad roaoal moos of he body. he kecs of he parcle, we foud ha wo force equaos of moo were requred o defe
More informationPosterior analysis of the compound truncated Weibull under different loss functions for censored data.
INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg
More informationQuality Monitoring Calibration Assuring Standardization Among Monitors
Qualiy Moioig alibaio Assuig Sadadizaio Amog Moios MOR Rspod oopaio Wokshop Spmb 2006 Ral Soluios fo Tlpho Suvy Mhodology alibaio - accodig o Wbs To sadadiz by dmiig h dviaio fom a sadad as o ascai h pop
More information( i IMPACT OF LONGITUDINAL AND TRANSVERSE WAVES BY CYLINDRICAL LAYERS WERE LIQUID 2 ~ t (1)
Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - IPT OF ONGITUIN N TRNSVRS WVS INRI RS WR IQUI I.I.Safaov Z.I olav.sh hmdov haa Tchologcal- Is of gg Rpblc of Uzbsa s. K. azayv 5 safaov5@mal.
More informationLet's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = =
L's rvs codol rol whr h v M s rssd rs o h rdo vrl. L { M } rrr v such h { M } Assu. { } { A M} { A { } } M < { } { } A u { } { } { A} { A} ( A) ( A) { A} A A { A } hs llows us o cosdr h cs wh M { } [ (
More informationImproved Exponential Estimator for Population Variance Using Two Auxiliary Variables
Improvd Epoal Emaor for Populao Varac Ug Two Aular Varabl Rajh gh Dparm of ac,baara Hdu Uvr(U.P., Ida (rgha@ahoo.com Pakaj Chauha ad rmala awa chool of ac, DAVV, Idor (M.P., Ida Flor maradach Dparm of
More informationChapter 5 Transmission Lines
ap 5 ao 5- aacc of ao ao l: a o cou ca cu o uppo a M av c M o qua-m o. Fo M o a H M H a M a µ M. cu a M av av ff caacc. A M av popaa o ff lcc a paal flco a paal ao ll occu. A ob follo ul. ll la: p a β
More informationNon-Equidistant Multi-Variable Optimum Model with Fractional Order Accumulation Based on Vector Continued Fractions Theory and its Application
QIYUN IU NON-EQUIDISN MUI-VRIE OPIMUM MODE WIH FRCION ORDER... No-Equds Mu-V Ou Mod w Fco Od ccuuo sd o Vco Coud Fcos o d s co Qu IU * D YU. S oo o dcd Dsg d Mucu o Vc od Hu Us Cgs Hu 8 C. Cog o Mcc Egg
More informationChapter 5 Transient Analysis
hpr 5 rs Alyss Jsug Jg ompl rspos rs rspos y-s rspos m os rs orr co orr Dffrl Equo. rs Alyss h ffrc of lyss of crcus wh rgy sorg lms (ucors or cpcors) & m-ryg sgls wh rss crcus s h h quos rsulg from r
More informationHygienic Cable Glands
ygc bl Gld followg h cll WA l h Mufcug h l oo c y Bocholog du hcl du: vodg buld-u cy. Gl bl ygc l food d d ckgg of ology y o o d u of ud ll ld hcucl wh hy ovd h f u o h cl o h o dh ooh fh No hd cod o d
More informationSchool of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines
Ogs of Quatu Thoy Masuts of sso of lght (EM adato) fo (H) atos foud dsct ls 5 4 Abl to ft to followg ss psso ν R λ c λwavlgth, νfqucy, cspd lght RRydbg Costat (~09,7677.58c - ),,, +, +,..g.,,.6, 0.6, (Lya
More informationChapter 21: Connecting with a Network
Pag 319 This chap discusss how o us h BASIC-256 wokig sams. Nwokig i BASIC-256 will allow fo a simpl "sock" cocio usig TCP (Tasmissio Cool Poocol). This chap is o ma o b a full ioducio o TCP/IP sock pogammig.
More informationdrawing issue sheet Former Royal High School - Hotel Development
H Forer oyal High chool - Hotel Developent drawing isse sheet general arrangeents drawing nber drawing title scale size L()1 ite Plan 1:1 / L()1 egent oad level proposed floor plan 1: 1 / L() ntrance level
More informationChapter 1 Basic Concepts
Ch Bsc Cocs oduco od: X X ε ε ε ε ε O h h foog ssuos o css ε ε ε ε ε N Co No h X Chcscs of od: cos c ddc (ucod) d s of h soss dd of h ssocd c S qusos sd: Wh f h cs of h soss o cos d dd o h ssocd s? Wh
More informationGauge Theories. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year
Gau Thors Elmary Parcl Physcs Sro Iraco Fomoloy o Bo cadmc yar - Gau Ivarac Gau Ivarac Whr do Laraas or Hamloas com from? How do w kow ha a cra raco should dscrb a acual hyscal sysm? Why s h lcromac raco
More informationComputational Simulations and Experiments on Vibration Control of a Flexible Two-link Manipulator Using a Piezoelectric Actuator
Egrg Lrs, 3:3, EL_3_3_ Compuaoal Smulaos ad Exprms o Vbrao Corol of a Flxbl Two-lk Mapulaor Usg a Pzolcrc Acuaor Abdul Kadr Muhammad, Shgo Okamoo, Ja Hoo L, Mmbrs, IAENG Absrac Th purposs of hs rsarch
More informationBeechwood Music Department Staff
Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d
More informationHeat Transfer in Unsteady Axisymmetric Rotational Flow of Oldroyd Liquid
aoal Joual of Scfc & Egg Rsach Volum, ssu 9, Smb-0 SSN 9-558 Ha Tasf Usady Axsymmc Roaoal Flow of Oldoyd Lqud A. Msha, G. S. Ray, S. Bswal Absac - Ths a dals wh h sudy of ha asf usady axsymmc oaoal flow
More informationIntegrated Optical Waveguides
Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla
More informationChain DOUBLE PITCH TYPE RS TYPE RS POLY-STEEL TYPE
d Fr Flw OULE IC YE YE OLY-EEL YE Oubard wh d s (d ) s usd fr fr flw vya. Usually w srads ar usd h qupm. d s basd sadard rllr ha wh sd rllrs salld xdd ps. hr ar hr yps f bas ha: (1) ubl ph rllr ha wh sadard
More informationCBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.
CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.
More information". :'=: "t',.4 :; :::-':7'- --,r. "c:"" --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'.
= 47 \ \ L 3L f \ / \ L \ \ j \ \ 6! \ j \ / w j / \ \ 4 / N L5 Dm94 O6zq 9 qmn j!!! j 3DLLE N f 3LLE Of ADL!N RALROAD ORAL OR AL AOAON N 5 5 D D 9 94 4 E ROL 2LL RLLAY RL AY 3 ER OLLL 832 876 8 76 L A
More information3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
More informationThe Linear Regression Of Weighted Segments
The Lear Regresso Of Weghed Segmes George Dael Maeescu Absrac. We proposed a regresso model where he depede varable s made o up of pos bu segmes. Ths suao correspods o he markes hroughou he da are observed
More informationPOSITIVITY AND REACHABILITY OF FRACTIONAL ELECTRICAL CIRCUITS
asz Kaczo Posy a achably o Facoal Elccal cs POSIIVIY ND EHIIY OF FION EEI IUIS asz KZOEK* *Facly o Elccal Egg ałyso Usy o chology l Wsa D - ałyso aczo@sppwpl bsac: oos o h posy o acoal la lccal ccs copos
More informationSIMULTANEOUS METHODS FOR FINDING ALL ZEROS OF A POLYNOMIAL
Joual of athmatcal Sccs: Advacs ad Applcatos Volum, 05, ags 5-8 SIULTANEUS ETHDS FR FINDING ALL ZERS F A LYNIAL JUN-SE SNG ollg of dc Yos Uvsty Soul Rpublc of Koa -mal: usopsog@yos.ac. Abstact Th pupos
More informationANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2
Joh Rley Novembe ANSWERS O ODD NUMBERED EXERCISES IN CHAPER Seo Eese -: asvy (a) Se y ad y z follows fom asvy ha z Ehe z o z We suppose he lae ad seek a oado he z Se y follows by asvy ha z y Bu hs oads
More informationA011 REF LANDSCAPE / CIVIL FOR INFO DRAWING NOT FOR CONSTRUCTION ARCHITECTURAL SITE PLAN ARLINGTON PUBLIC SCHOOLS
S D S X JS K D L PUBL SLS LY SL # S S JS DDL SL South ld lebe d rlington, lient Project umber Y B LL J L.. 79 L D Project umber PD D hecked By " 9'- 9 " 9'" 9'- 9 " 9'" 9'" 9'- LDSP / L " 9'- 9 PJ (8.
More informationBUDA TOWN CENTER CLICK FOR DRONE VIDEO. PJ KAMINER
CICK FO DONE VIDEO UDA TON CENTE PJ KAMINE 5.485.0888 pkm@oo. ANCE MOIS 5.485.0888 mo@oo. INTODUCTION T Coo p o p foowg oppouy o pu 00%, mu- vm u, Tx. u 00, ubj popy w-ou, fg,,39 SF bug ow-o by m Sup.
More informationBUDA TOWN CENTER CLICK FOR DRONE VIDEO. PJ KAMINER
CICK FO DONE VIDEO UDA TON CENTE PJ KAMINE 5.485.0888 pkm@oo. ANCE MOIS 5.485.0888 mo@oo. INTODUCTION T Coo p o p foowg oppouy o pu 00%, mu- vm u, Tx. u 00, ubj popy w-ou, fg,,397 SF bug ow-o by m Sup.
More information_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9
C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n
More information9.6 Spherical Wave Solutions of the Scalar. Chapter 9: Radiating Systems, Multipole Fields and Radiation
Cha 9: Raag Syss, Muo Fs a Raao A Ovvw of Chas o EM Wavs :(ov hs ous sou wav quao bouay Ch. 7 o a wav sa o wo s- sas saa by h - y a Ch. 8 o oug was - Ch. 9 J, ~ ougog g wav o sb, as a aa - Ch. J, ~ ougog
More information