Chpte # Deg of e Cotol Ste Itodcto to tte pce Obevblt/Cotollblt Modle ede: D D o - d.go@cl.c.k /
Itodcto e th ode te: ( ) ( ) ( ) '',... ',, f. Ve dffclt to be tded (theoetcll we c e geoetc d/o ltc ethod) > o we e copte. Copte e bette wth t ode ODE > bek the th ode to te of t ode. lo b g tce we c e powefl tool fo the le lgeb! Eple: e the ple, pg te: Ug Newto echc we get: k F d F d choog we hve:, ( ) F k k F O U F k Modle ede: D D o - d.go@cl.c.k /
Now, ode to oto the te we eed eo to ee vo vble lke the dplceet d veloct of the. et e tht we c b both eo, the we defe the otpt of the te to be: C Y Y et e tht we c b ol oe eo, tht ee the dplceet, the the otpt : [ ] C Y Y et e tht we c b ol oe eo, tht ee the veloct, the the otpt : [ ] C Y Y et e tht we hve ol oe eo tht ee le cobto of the dplceet d veloct: [ ] C Y Y Hece, the ot geel ce (fo the bove eple): C Y Y b b b b Modle ede: D D o - d.go@cl.c.k /
Fll let e tht ( the tfcl ce) tht the pt c dectl flece the otpt, the we hve: C DU, Fo oe t D. U So the te decbed b : C DU U C DU eell I c hve oe th oe pt d/o otpt: U C DU O vecto fo: U C DU Whee: U M, Y q p Modle ede: D D o - d.go@cl.c.k 4/
I geel: ( () t ( ( U( Y( C( ( D( U( Whee tte vecto U q pt vecto Y p otpt vecto tte t q pt t C p otpt t D p feed fowd t (ll zeo) If the te e e Ivt (I): ( ( U( Y( C( DU( U D Y C he tte vecto decbe the te > ve t tte > he tte of te coplete of the te t ptcl pot te. If the cet tte of the te d the fte pt gl e kow the t poble to defe the fte tte d otpt of the te. he choce of the tte pce vble fee log oe le e followed: he t be lel depedet. he t pecf copletel the dc behvo of the te. Fll the t ot be pt of the te. Modle ede: D D o - d.go@cl.c.k 5/
Eple of tte pce odel (NO SSESSED MEI) Eple e the followg ple electoechcl tht cot of electoget d he foce of the getc feld dectl elted to the cet the etwok. he foce tht eeted o the object f k, whee k potve cott. o plf the l we e tht the dplceet ve ll d tht ll e the cet h le eltohp wth the foce: f k Ug cct theo: ( v ) d Ug Newto d lw: f k k k Now, we c defe, ( v ) d. h: v Modle ede: D D o - d.go@cl.c.k 6/
k k k k Hece the tte pce odel : v k k Now let e tht we hve ol oe eo tht wll et the dplceet : [ ] h the tte pce odel : [ ] v k k Modle ede: D D o - d.go@cl.c.k 7/
Eple othe eple how the et fge. he hft of the eptel ected DC oto coected to the lod J thogh ge bo. ϕ ϕ ϕ ϕ d v d v J J, ϕ ϕ ϕ ϕ d v J d v J I defe :, Modle ede: D D o - d.go@cl.c.k 8/
v J J v J J v J Eple It c be poved tht odel of the Idcto Mche : ( ) ( ) ( ) ( ) d d d d ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ Modle ede: D D o - d.go@cl.c.k 9/
O: q d q d q d q q d d q d q d d d d d d d d d Modle ede: D D o - d.go@cl.c.k /
Stte pce he te tte c be wtte vecto fo : [,, ] [ ] [,,, ],,,,,,, > tdd othogol b (ce the e le depede fo - deol vecto pce clled tte pce. Eple of tte pce e the tte ple () d tte D pce (), Modle ede: D D o - d.go@cl.c.k /
Mtlb d SS odel >> [ ;- -.5]; >> [ ]'; >> Cee(); >> D; >> _odel(,,c,d) - -.5 b c d Coto-te odel. Modle ede: D D o - d.go@cl.c.k /
elto of tte pce d F (NO SSESSED MEI FO EEE8) If we hve I tte pce () te, how c we fd t F? ( ( U( ( ) () ( ) U( ) ( I ) ( ) U( ) () ( ) ( I ) U( ) ( I ) () d fo the d eqto of the te: Y ( ) C( ) DU( ) > Y( ) C ( I ) U( ) ( I ) () ) DU( ) ( C( I ) D) U( ) C( ) () Y( ) I defto F: the IC. ( I ) D d C( I ) () C the epoe to lo: ( ) ( I ) U( ) ( I ) {( I ) U( ) } ( I ) ( t ) { } () { I } If U > ( ) ( I ) t o : ( ) I () { } () t bt we hve ee tht ( t ) e () e. t Modle ede: D D o - d.go@cl.c.k /
So the F. Fo le lgeb: () ( ) D I C () I D C I d hece I the CE of the F!!! () ( ) I C D I > the F t! So: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( pq p p q q...,,, U Y U Y U Y U Y Eple: Fd the F of d.5 [ ] >> [ ;- -.5]; [ ]'; C[ ]; D; >> [,de]tf(,,c,d) -.. de..5. Modle ede: D D o - d.go@cl.c.k 4/
>> tep(,de) >> tep(,,c,d).5 Step epoe pltde.5 5 5 5 e (ec) Modle ede: D D o - d.go@cl.c.k 5/
Obevblt e tht we hve the followg te: [ ]. Notce tht the odel copled d ce C t poble to ee how behve (o poble f w ot dgol o C w ). h ple tht we cot oto, fo eple t c dvege to ft wth cttophc elt fo o te. NO SSESSED MEI e tht we hve othe te: Clel thee two odel e dffeet. I tht ce t c be poved tht the te hve the e tfe fcto d lo thee pole-zeo ccelto [ ] 6 [ ] [ ] Modle ede: D D o - d.go@cl.c.k 6/
[ ] ( )( ) [ ] ( ) ( )( ) [ ] 6 whch ectl the e the F of the ft te, wht wog? hee pole zeo ccellto t the ecod odel (o fd the zeo t odel e D C I ): >> [- ; -]; [ ]'; C[ ]; D; >> _odel(,,c,d); >> [P,Z] pzp(_odel) P - - Z -. ( ) D C I d the pole of the te: ( )( ) I he ccellto de to C[ ]. Modle ede: D D o - d.go@cl.c.k 7/
Cotollblt e tht we hve the followg te: [ ] I th ce we c ee how both tte behve bt we c ot chge U w o tht we c flece de to the fo of. If w ot dgol we wold be ble to cotol thogh. NO SSESSED MEI Sll we hve pole-zeo ccellto : [ ] [ ] ( )( ) ( ) ( ) ( ) 6 >> [- ; -]; [ ]'; C[ ]; D; >> _odel(,,c,d); >> [P,Z] pzp(_odel) P - - Z - Modle ede: D D o - d.go@cl.c.k 8/
Hece the ft ce b popel defg U we c cotol both tte bt we cot ee the ecod tte, whle the ecod ce we c ee both tte bt we cot cotol the ecod tte. he ft te clled obevble d the ecod cotollble. he lo of the cotolblt d/o obevblt de to pole/zeo ccellto. hee te e cceptble d the olto to tht poble to e-odel the te. he te tht e both cotollble d obevble e clled l elto. We eed to develop tet to detee the cotollblt d obevblt popete of the te. Dffclt tk f the te ole. I o ce we pl hve to fd the k of two tce. Fo obevblt: M O C C C M C obevble. Fo cotollblt:. If the k of th t le th the the te M C [ ]. If the k of th t le th the the te cotollble. Modle ede: D D o - d.go@cl.c.k 9/
Mtlb Eple: >> [- ; -]; [ ]'; C[ ]; D; >> k(obv(,c)) >> k(ctb(,)) >> [- ; -]; [ ]'; C[ ]; D; >> k(obv(,c)) >> k(ctb(,)) >> [- ; -]; [ ]'; C[ ]; D; >> k(obv(,c)) >> k(ctb(,)) Modle ede: D D o - d.go@cl.c.k /