Instructor: J.D. Williams, Assistant Professor Electrical and Computer Engineering
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- Berenice Baldwin
- 6 years ago
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1 EE 4/5: Eecoechnc e T/Th :45 :5 PM TH N55 Inco: J.D. W, An Pofeo Eecc n Cope Engneeng Une of Ab n Hne 46 Opc ng, Hne, A 5899 Phone: , e: w@eng.h.e Coe e poe on UAH Ange coe ngeen webe Teboo:.E. he, Eecoechnc e n Dece, CRC Pe, 8 IN Nbe: Opon Reng: H.D. Ch, Eecoechnc Moon Dece, Pence H, 998.J. Chpn, Eecc Mchne Fnen, 4h e. McGw H, 5.E. he, Engneeng n cenfc Copon ng MATA, We, A.E. Fzge, C. Knge,.D. Un, Eecc Mchne, 6h e. McGw H, C.W. e, Mechonc: n Inege Appoch, CRC Pe, 4 5// A fge en fo p eboo ne ohewe ce.
2 EE 4/5 - Eecoechnc e: Coe Me Chpe : Inocon o Eecoechnc e Chpe. An of Eecoechnc e Reew of Eecognec Reew of Cc Mechnc Inocon o MATA n n Chpe. Inocon o Powe Eeconc Moeng n Appcon of Op. Ap., Powe Apfe, n Powe Conee Chpe 4. DC Eecc Mchne n Moo Dece Geoe n Eon of Moon Goenng DC Eecc Moo Moeng n on of DC Eecc Moo Penen Mgne DC Geneo DC Eecc Mchne wh Powe Eeconc A Topoog of DC Eecc Mchne n Mgnezon Cen Chpe 5. Incon Mchne oe nce opc Oeew Phe AC Incon Moo Eon of oon fo Phe AC Incon Moo Toe Chcec Phe ncon oo Inocon o Qe n Dec Vbe Ab Refeence Fe on of n Phe AC Incon Moo ng MATA n n Chpe 6. nchono Mchne nce opc Inocon nge n Thee Phe Recnce Moo Two n Thee Phe Penen Mgne nchono Moo n eppe Moo MATA n n on Chpe 7. Inocon o Cono of Eecoechnc e n PID Cono w Eon of Moon Goenng he Dc of Eecoechnc e Anog PID Cono w n ppcon nong Penen Mgne DC Moo Dg PID Cono w n ppcon nong eoe wh Penen Mgne DC Moo 5//
3 EE 4/5 - Eecoechnc e: Coe Agnen Hoewo: Hoewo w be gne hogho he eee n e 7 fe gnen. Agnen w be ge n ene o ccon fo % of he fn coe ge. E: Two n c e w be gen ng he eee. en w be owe he e of cco ng he e. A wo w be pefoe nepenen. Ech e w ccon fo 5% of he en ge. The fn e w be copehene coeng jo opc peene hogho he eee n w cone % of he coe ge. Fn Ge: Hoewo Wee % E pe eee 5% Fn Copehene % 5//
4 EE 4/5: Eecoechnc e Chpe n Chpe : Inocon o Eecoechnc e Chpe : An of Eecoechnc e n Dece Inocon o n n oeng Eneg coneon n Foce Pocon Oeew of eecognec Oeew of cc echnc Newonn echnc on Appcon of cobne e on of e n he MATA enonen 5// 4 A fge en fo p eboo ne ohewe ce.
5 Inecpn Appoch o Eecoechnc e Engneeng fgf fgf fgf fgf fgf Knec Eneg Poen Eneg 5// 5
6 Moen Eecoechnc Dece 5// 6
7 Inecpn Appoch o Eecoechnc e Engneeng 5// 7
8 Pon Chge Dbon n Coob w The foce, F, beween wo pon chge Q n Q : Aong he ne jonng he Dec popoon o he poc beween he Inee popoon o he e of he nce beween he 4 Whee, o F o QQ 4 o R The eon boe e cce fo e chge, Q, he ogn n oce chge, Q, nce R w. The oon gh oe copce we oe o efeence fe w fo he wo chge ch h Q efeence b he eco n Q efeence b he C / N 5// 8
9 G w G w: The eecc f,, hogh n coe fce e o he o chge encoe b h fce, h =Q enc Ineg Fo D Appng he egence heoe, we he eng he ffeen fo D Q enc D D Th he f of he 4 Mwe Eon whch ce e h he oe chge en e o he egence of he eecc f en Mwe Eon In e D D E H J 5// 9
10 G w G w p n ene een of Coob w. G w poe n e en of fnng E o D fo ec chge bon Appcon: Pon Chge D D n Q D Q Q enc enc enc D Q 4 D D n n D4 5// Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
11 Eecc Poen We efne he eecc poen o he oon c fe, V, ecbng n eecoc eco fe, E, he gne of he ffeence beween E wo pon n b n oe n coon efeence pon o. p V p E nege e b conenon o V b V o b o E Now, he Gen heoe e h V E V E co E V V E o E b E Noe he cc oe h nepenence of ph p: If E w epenen on ph, hen he efnon of V wo be nonene bece he ph wo e he e of Vp 5//
12 The Deecc Conn I pon o noe h p o h pon, we he no coe oee o he ce of he pozon, P. We e on wh effec. We he e h he pozon of eecc on e fo n eecc fe whch ne p he oc o oec poe. In n bnce, epeen eence how h he pozon popoon o he eecc fe, poe h E no oo ong. Thee bnce e o he ne, oopc eecc conn Th popoon conn ce he eecc cepb, e. The conenon o ec he pe of fee pce fo he eecc cepb o e he n enone. Th we he Fo he peo e D oe P o e E D o E D E P ee o The eecc conn o ee pe of he e,, he o of he pe o h of fee pce If he eecc fe oo ong, hen begn o p eecon copee fo oece eng concon effec. Th ce eecc beown. The engh of he eecc h eecc cn oee po o whch beown occ ce he eecc engh. 5//
13 Ung G w Wh Deecc Ung G w Wh Deecc Concenc Concng phee wh b b> wh eecc f Two f conce pe of e A fe wh eecc E E E, b b> wh eecc f e, A, fe wh eecc z R Q E o R Q D E E D E E E enc z o z o z o E E b Q D V b o A Q D V Q DA D z o E b Q Q o 4 A b 4 5// If cpcnce, C=Q/V, hen wh he e fo ech epe? Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
14 Conn Eon Reebeng h chge conee, he e e of ecee of chge whn gen oe be e o he ne ow fow hogh he fce of he oe Th, he cen o of coe fce Appng oe Theoe Q I J J J J encoe Conn Eon Fo e e pobe, he ee of chge wh epec o e e zeo, n h gen of cen en he fce zeo, howng h hee cn be no ne ccon of chge. 5// 4
15 Eecc Ree Cone conco whoe en e nne poen ffeence.e. he eecc fe whn he conco nonzeo n fe pe hogh h he e. Noe h hee no c eb n h e. The conco beng fe eneg b he ppcon of he eecc fe b poen A eecon oe whn he e o e p ncon fe, he ce n e heefoe pe. Th png nfe he ence, R, of he e. Fo h epe e: R nfo co econ e, n engh. The econ of he eecc fe, E, poce he e he econ of fow of poe chge o he e he cen, I. V I E E E V I J V R I V E c 5// 5 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
16 Cpcnce Cpcnce he o of he gne of chge on wo epe pe o he poen ffeence beween he C Q V E E Noe h V E The nege gn oppe n he efnon boe bece we e neee n he boe e of he oge op Cpcnce obne b one of wo eho Ang Q, n eene V n e of Q Ang V, n eene Q n e of V If we e eho, e he foowng ep Chooe be coone e e he wo concng pe c chge +Q n Q Deene E ng Coob o G w n fn he gne of he oge, V, negon Obn C=Q/V 5// 6 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
17 Cpcnce. Rence R V I Q R V RC E E E E C, R b n C, R b n b C 4, R 4 b C 4, R 4 Pe Pe Co Cne eween phee Ioe phee 5// 7
18 Dg of Eecoc Dg of Eecoc V o 4 E o 4 E E o o V E V E V 5// 8 E V E V Fge ecope fo Gffh, Inocon o Eeconc, e., enjn Cng, 999.
19 o- w The ffeen gnec fe nen, H, poce pon P, b he ffeen cen eeen, I, popoon o he poc I n he ne of fhe nge beween he eeen n he ne jonng P o he eeen n nee popoon o he e of he nce, R, beween P n he eeen H I ˆ 4 R R I 4 R R I n 4 R 9 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
20 Apee Cc w Apee w: The ne neg of H on coe ph he e he ne cen, I enc, encoe b he ph H o G w nce Apee w e e o eene H when he cen bon ec Apee w AWAY ho, een f he cen bon NOT ec, howee he eon on e effece fo ec ce e G n Coob w, Apee w pec ce of he o- w n cn be ee ec fo. I enc Appng oe heoe poe ene oon eho I I enc enc H H J Defnon of Cen poe n Chpe 5 H J Mwe En.
21 Dpceen Cen e now ene e epenen fe fo he pepece on Apee w. H J H J Th eco en fo he co poc hec J. Howee, ee h he conn en. e zeo, whch no fo n eecoc npon! H J J Th, e n on cen en e o bnce he eecoc fe eeen H J J D J J D D We cn now efne he pceen cen en J he e ee of he pceen eco D H J Anohe of Mwe fo e ng fe Th one ee Mgnec Fe Inen o concon n pceen cen ene 5//
22 Mgnec F Den Mgnec F en,, he gnec een of he eecc f en, D. A ch, one cn efne, Apee w I enc whee An he Mgnec f hogh fce H 4 ˆ The gnec f hogh n encoe e 7 Defnon of oeno fe n Mwe 4 h en. H / H
23 F w We he noce ee eho of enng gnec fe n e of foce, eneg, n ncnce. Mgnec fe ppe o be ec e of chge ong hogh h e n eone eee fe oon fo poe, n bon conon pobe. o no ogc o ep o oe gnec fe n e of n eecc one? Th he eon e b Mche F n Joeph Hen n 8. The e F w fo nce ef Ince eecooe foce ef n o n n coe cc e o he e e of chnge of gnec f b he cc V ef N whee, befoe, he f nge, he gnec f, N he nbe of n n he nco, n epeen e ne. The nege gn how h he nce oge c o oppoe he f pocng. The een n be boe nown enz w: he nce oge c o oppoe he f pocng. Epe of ef genee eecc fe: eecc geneo, bee, heocope, fe ce, phoooc ce, nfoe. 5//
24 F w To eboe on ef, e cone be cc. The eecochec con whn e n n ef poce eecc fe, E f Acne chge he en poe n eecoc fe E e h o e h conec he ef genee poen E E f E e E E f P E IR The o ef genee n b e epenen oon o gnec fe Vef E E Noe he foowng pon fc N An eecoc fe cnno nn e cen n coe cc nce E IR An ef-poce fe nonconee e f Ecep n eecoc, oge n poen ffeence e no een 5// 4 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
25 Inco n Incnce We now now h coe gnec cc cng cen I poce gnec fe wh f We efne he f nge beween cc wh N enc n N A ong he e he f pe hogh ne oopc hen hen f nge popoon o he cen I pocng n cn be wen Whee conn of popoon ce he ncnce of he cc. A cc h conn ncnce o be n nco. One cn ee he ncnce o he gnec f of he cc I I N I whee ee n n of Hen H = Wb/A The gnec eneg n Joe oe b he nco epee W I 5// 5 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
26 Inco n Incnce nce we now h gnec fe poce foce on neb cen eeen, n h hoe gnec fe cn be genee b n oe o cope e of cen cng cc, hen on eonbe h ch cc nce fe n gnezon beween he We cn cce he n f nge beween he wo coponen ewe we cn eene ncnce beween he cc h e fo cc fo cc N M I I In ncnce e N N I I I I The o gnec eneg n he cc 5// W W W W I I M II 6 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
27 Inco n Incnce A we ee o befoe, o ho hn of n nco conco hpe n ch w o oe gnec eneg Tpc epe nce oo, oeno, co non ne, n pe-we non ne One cn eene he ncnce fo gen geoe ng he foowng echne Chooe be coone e e he nco c cen, I Deene fo o- o Apee w n cce he gnec f Fn fncon of he f e he nbe of n oe he cen ce M ncnce be cce b ppoch Deene he nen ncnce, n fo he f genee b he f nco Deene he een ncnce, e poce b he f een of he f nco The of he nen n een ncnce e he n ncnce p he ncnce beween he eeen N M I I Fo cc heo, we cn o gh he ncnce whch poe e ef eon when c ppng o eeconc cc C RC R R 5// 7 e e e
28 Foce De o Mgnec Fe Foce De o Mgnec Fe Rec h he foce on chge pce p F=E If he pce oe howee hen n on foce poe fo he chge If he pce oe howee, hen n on foce poe fo he chge pceen of eoc,, nfe b he gnec fe,. The cobne foce ce he oenz w: E F Rec fo Newon w h E F E F The nec eneg of chge pce n n gnec fe heefoe F Fo,, n n ohogon econ, One cn ece coone e n whch F z z z z ˆ Ccoon Reonnce Feenc 5// 8 KE z z The ocon of he pce cn o be fon Feenc
29 oenz Foce w Rec h he foce on chge pce p F=E If he pce oe howee, hen n on foce poe fo he chge pceen of eoc,, nfe b he gnec fe,. The cobne foce ce he oenz w: F Rec fo Newon w h E F E The nec eneg of chge pce n n eecc fe heefoe The ocon of he pce cn o be fon F E E E 5// E z z KE 9
30 Mgnec Toe n Moen Now h we he ene he foce on cen cng oop. e ene he Toe ppe o Toe, T, on he oop he eco poc of he foce, F, n he oen,. n fo nfo F I T Iw n eng T I n T F Whee we cn now efne n T F n he gnec poe oen wh n A/ whch he poc of he cen n e whee of he oop n he econ no he fce e efne b he oop F I I ˆ ˆ zz zz F F I ˆ n 5// T b w Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
31 Toe n Dpoe Popee of Mgne A b gne o fen oop gene efee o gnec poe Ae b gnec of engh,, genee nfo gnec fe,, n poe oen, =Q Toe, T, on he oop he eco poc of he foce, F, n he oen,. Th, bece he b gne epeen gnec poe oen e n gne o he poe oen of cen oop, b gne cn o be en gnec poe T Q F Q T Q I Q I Theefoe he fe eonbe nce w fo n b gne hec 5// enc o h of poe. Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
32 Mwe En. fo c Fe Dffeen Fo Ineg Fo Re D E H D J E H J G w Noneence of he Mgnec Monopoe Conee ne of he Eecc Fe Apee w 5//
33 Mwe Te Depenen Eon I w Je C Mwe h p of h ogehe n ece eecognec fe heo o 4 pe eon. I w on hogh h cfcon h he coe of eecognec we wee coee n he heo of gh w eeope. The eon Mwe cee wh o copee ecbe n eecognec fe ehe c o nc e wen : Dffeen Fo Ineg Fo Re D D E E D D H J H J G w Noneence of he Mgnec Monopoe F w Apee Cc w 5//
34 Anog eween ee Eecc c n Mgnec Fe c w Foce w oce Eeen Fe nen F en Eecc Q Q F 4 D Q F Q E Q ˆ D C / Reonhp eween Fe Poen F Eneg Den Poon En. E D E V E V V enc / V 4 D Q CV V I C w E D E V Mgnec I ˆ 4 R H I enc F Q Q I I H A / Wb / H H V, J I A 4 R I I I w E H A J 4
35 Eecognec Wo n Powe Eecognec Wo n Powe e e D D E E W w Eecc eneg en T w w w H H W w Mgnec eneg en T e T H E D w W w w w Eecognec eneg E H E D H E P To eecognec powe = e of ecee n oe eneg ohc powe pe 5// 5
36 Eecoc on Conon Eecoc bon conon fo E n D cong n e nefce ch he foowng conon eeope ng G w n coneon of he eecc fe Two ffeen eecc chceze b n. D D Q enc E E D n D D n D E n En E E 5// 6 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
37 Mgnec on Conon Mgnec bon conon fo n H cong n e nefce ch he foowng conon eeope ng G w fo gnec fe n Apee cc w Mgnec on Conon foowng conon eeope ng G w fo gnec fe n Apee cc w I H I H I H H H n n 5// 7 n n H H Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
38 Mwe Te Depenen Eon: Ien Mp 5// 8 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
39 Cfcon of Mgnec Me In gene we e he gnec cepb o ee peeb o cf e n e of he gnec pope A e o be nongnec f hee no bon cen en o zeo cepb. Ohewe gnec Mgnec e be gope no hee ce, gnec, pgnec, n feognec Fo n pcce ppoe, gnec n pgnec e ehb e o no gnec cepb. Wh gnec popee hee e o he foow ne epone oe ge nge of ppe fe Feognec e ep beow he Ce epee ehb e ge nonne gnec cepb n e e fo conenon gnec ece ppcon 5// 9 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
40 Cfcon of Mgnec Me Dgne Occ when he gnec fe n he e e o n eecon oen cnce ech ohe o. Th he penen gnec oen of ech o zeo. ch e e e we ffece b gnec fe. Dgnec e nce Coppe, h, con, on, n o choe be In gene h effec epee nepenen. Th, fo epe, hee no echne fo gnezng coppe peconco ehb pefec gne. The effec o ong h gnec fe ppe co peconco o no penee oe hn few oc e, eng n = whn he e Pgne Me whoe o ehb gh non-zeo gnec oen Pnge epee epenen Mo e, ngen, po, one ehb pgnec effec h poe gh gnezon n he peence of ge fe ow epee 5// 4
41 Cfcon of Mgnec Me Feogne Occ n o wh ee ge gnec oen Epe: Cob, Ion, Nce, o o be on hee hee Cpbe of beng gneze e ong b gnec fe Ren conebe on of he gnezon when eoe fo he fe oe he feognec popee p n becoe ne pgnec e non gnec when he epee e boe cc epee ce he Ce epee. The gnezon nonne. Th he cone eon = H oe no ho bece epen ec on n cnno be epeene b nge e. Feognec heng Feognec e cn be e o foc n ge he fow of ncen gnec fe pcng feognec e copee on ece, one cn he ece fo n een fe. Th heng occ b/c he feogne c gnec wege, h n he fe on he hpe of he ce n no whn. 5// 4 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
42 Cfcon of Mgnec Me 4 Feogne - -H Ce The gnezon of feogne n n een ppe fe, H, peene beow. A H ncee, he gnec fe,, whn he e ncee gnfcn n hen begn o e o e e H ppoche H A he ppe fe, H, eoe, he feognec e en oe egee of gnezon n he pon whch he ppe fe H copee eee whch e he gnec fe ne he e e o he The ppe fe hen ncee gn o genee he copee Hee ce Two ohe efnng e e nce of ee -H gnezon Hee ce. When he ppe fe e n hen gn ece o zeo e. The gnec fe whn he e en oe poe e efee o he penen f en. The e pon whch becoe zeo ne n ppe H e ce he coece fe nen, H c Me wh coece fe nen e e o be of gnec e n o no en gnfcn gnezon pon he eo of he fe H gne penen gne he e ge coece fe nen e 5// 4 Fge fo: M.N.O., Eeen of Eecognec 4 h e. Ofo Une Pe, 7.
43 Mgnec Popee of Coon Me 5// 4
44 Mgnec Popee of Coon Me 5// 44
45 Reew of Newonn Mechnc e ec he of cc Newonn echnc n whch Dnce ˆ ˆ ˆ z oe fo one ocon o nohe n Cen coone e The phe wh foce, F,, e o e cceeon,. The wo one pon he he ne ph nepenen ne neg of F ong he coe cono An we cn efne he e b he on of eneg ee o oe he eoc,, p he poen eneg of he o oe who n een e Veoc Acceeon To Foce Wo Done z z z z z z z Poen Gen p F, W W F, ewe, foce b nce. W F, F,, F 5// 4 Eneg of he e: Knec n Poen 5
46 Poen Eneg Knec Eneg Epe of Mechnc Foce n Wo Epe Cone poonng be ce b oo e fn o how ch wo one o cceee g po wh = g fo = o f = /.. J W f Epe Cone,, co f fce n Cen coone e The foce, F, ppe n oon occ n he econ Fn he eon of oon negecng coob n c fcon, howee nce co fcon F F F F f f e f oe ne ODE F 4 co 4 e F FN Fg 4 co 4 e, 5// F F F 46 f
47 Reew of Newonn Roon Mechnc One cn how fo oon ece h he oe, T, genee on n objec wh fe oon engh R oe n e nne o ne pceen n oon T, J J J of Toe n -D Ang oen, R p R R Rec h he oon engh fe p T R p R R F J J Fo -D e, he of of he oen : M J whee J he oen of ne g* n he ng cceeon of he bo / 5// 47
48 Roon Mechnc Epe A oo h he een oen of ne, J=.5 g*. When he oo cceee, he ng eoc of he oo =,. Fn he ng oen n he oe fncon of e. T J.5 g / 5 5 N N 5// 48
49 Reew of Newonn Mechnc Cone he non oon of bo whch che o n e png h ee foce whch h obe Hooe w. Negecng fcon, one obn he foowng epeon fo eneg To eneg n he e Knec Eneg Poen Eneg E T he png conn Fo oon oon n oon png ET J J Fo non n oon oon n oon png J 5// 49
50 Reew of Newonn Mechnc The oen of ne J epen on how ch be wh epec o he. Th noe h J ffeen fo ffeen e of oon n w he o be ecce one chnge coone e o oon econ If he bo h nfo en, J cn be cce fo eg hpe boe ng he enon. Fo epe, g cne of, R, n engh, h he foowng hozon n ec oen of ne, J J J hozon ec R R 4 The of gon cn be fon fo eg hpe objec, n he oen of ne cn be e obne. ee n c hno 5// 5
51 Reew of Newonn Mechnc In eecoechnc oon ece, he foce n oe e of ge nee. Ang g bo n conn oen of ne one h Reew of Newonn Mechnc Ang g bo n conn oen of ne, one h The o wo one gen b J J J J T g j j J T W f f f Knec Eneg Fheoe, powe Th he nog of ppe fo non oon T T W P F P Th he nog of ppe fo non oon Epe: Ae he e powe n ng eoc of oo e W n /. The e eecognec oe fon o be F P 5// 5 N W P T. /
52 Fcon n Moon Dece ece o he ece ce n h coe e o echnc oon, con of fcon een Fcon hgh cope nonne phenoenon h pc pfe o ee of eon h ee p oe n he pefonce chcec of he e Fo o ppoe we w pf fcon no one of hee ffeen ecpon Coob fcon eng foce o oe h chnge gn wh he ee of he econ of oon. The eon of coob fcon e FCoob Fcgn TCoob Tcgn whee fc n Tc e he Coob fcon coeffcen fc Tc Vco fcon eng foce o oe h ne o nonne fncon of pceen n n Fco n Tco n n n whee n e he Coob fcon coeffcen c fcon e on when he bo on n nhe oon begn F c F T c T 5// 5
53 Fcon n Moon Dece Fo ee of he pobe peene whn h e, he foowng eon fo fcon w be ppe o poe ee ppng of phc e wh fcon eo, peng conon, ec. F T f f e f gn e gn f f f f f 5// 5
54 pe Pen A pon pene b e nechbe ng of engh. Dee he eon of oon F g n T ppe oe M g n T J J g n T En. of Moon: ne ODE g T n T J J g n T g n T J 5// 54
55 gngn Dnc gngn nc n eneg be echne ng geneze coone o eeop e obn eon of oon fo een he o copce of e I wo fo eneg be e n cn heefoe be e e n -on pobe ch eecoechnc pobe h nce eeconc cc, gnec f, oe, n een hc coponen o he e We b efnng he nec, pe, n poen eneg e n he e n,,..., n,,..., n D,,..., n,,...,,,..., n Knec Eneg Dpe Eneg non-conee Poen Eneg Whee e gene coone be che o he geoe of he e, n o he ee of wh epec o e he oen coponen. Q geneze foce e e o ee he coone e. Q The gnge g eon of oon hen efne D Q 5// 55
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