Note4 - !"#"$%! !"#$#%"#&'()*+,'-....

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!"#"$%%! & !" $ %" &’()*+,’-. /0+2,)3 1 4)-,’5(. 678 /5(.,+(, 9--):)3+,’5( ’( !;" ! <( !;" = >) ())? ,5 @))2 ,3+-@ 5A ! ! C) -+( ?).-3’D) ?’.2:+-)*)(, DE + !"#$%& F ! G0) .’*2:)., ,0’(H ,5 ?5 ’. ,5 -055.) + -553?’(+,) .E.,)* +(? .,I?E ,0) *5,’5( +:5(H )+-0 +J’. " r ! x ! i " y ! j KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. ! " ’B)B= ,5 3).5:P) ,0) *5,’5( ’(,5 -5*25()(,. ! QA -5I3.)= P):5-’,E +(? +--):)3+,’5( +3) P)-,53.= ,55F " v ! v x ! i " v y ! j ! dx dt ! i " dy dt ! j " a ! a x ! i " a y ! j ! d # x dt # ! i " d # y dt # ! j /5(.,+(, 9--):)3+,’5( ’( !;" ! R53 )+-0 -5*25()(,= ,0) *5,’5( -+( D) ?).-3’D)? I.’(H ,0) .+*) )SI+,’5(. +. A53 6;" *5,’5( ! DI, (5> r 3)2:+-). = v 3)2:+-). ! = +(? a 3)2:+-). ( KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. % ! R53 )J+*2:)F ! * ! N + ($ # ! * ! N= + ( $ $ ! , * ! N= , + ( , $ " >) (5> ())? )SI+,’5(. A53 )+-0 ?’3)-,’5( ! <A 25. .’D:)= >) .05I:? -055.) ,0) +(? , +J). .5 ,0+, ,0) .2))? +:5(H 5() 5A ,0)* ’. -5(.,+(, B
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!"#"$%%! $ T35U)-,’:) V5,’5( ! 9 ,E2’-+: )J+*2:) ! 9--):)3+,’5( ’. ?I) 5(:E ,5 H3+P’,E ! 4’(-) H3+P’,E 25’(,. ?5>( = KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. 1 ( W N ( , W 7 - ! G0) ’(’,’+: P):5-’,E P)-,53 -+( D) 3).5:P)? ’(,5 -5*25()(,. ! N=J W ! N -5. $ N ! N=E W ! N .’( N 0 subscripts mean initial values. T35U)-,’:) V5,’5( ’( !;" ! G0) @’()*+,’- )SI+,’5(. >) >35,) 23)P’5I.:E ’( 6;" D)-5*)= ’( -5*25()(, A53*F ’. v x ! v $% x " a x t ! v $ &’( V5,’5( +:5(H ,0) KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. X ,. x x $ ! v $% x t " # a x t # ! v $ &’( % & t v y ! v $% y " a y t ! v $ (*+ gt y y $ ! v $% y t " ) # a y t # ! v $ (*+ %& t ) # gt # v y # ! v $% y # " # a y y y $ ! v $ (*+ # # gy y $ +J’. ’. -5(.,+(, B T35U)-,’:) V5,’5( ! Key point: G0) 053’Y5(,+: *5,’5( 5A + 235U)-,’:) 0+. (5 )AA)-, 5( ’,. P)3,’-+: KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. Z *5,’5(F ,0) *5,’5(. +3) ’(?)2)(?)(, B
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!"#"$%%! ")*5F 4055, ,0) /+( ! G0) -+( +(? ,0) D+:: A+:: +, ,0) .+*) 3+,)= ,0)’3 053’Y5(,+: *5,’5(. +3) ’(?)2)(?)(,= +(? 0)(-) ’A KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. 8 3):)+.)? +, ,0) .+*) ,’*) >’:: -5::’?)B [I).,’5( 6N ! R’HI3) .05>. % 2+,0. 5A + A55,D+:: @’-@)? A35* H35I(? :)P):B ! <H(53’(H +’3 3).’.,+(-)= 3+(@ ,0) 2+,0. A35* H3)+,)., ,5 :)+., I.’(H +\ <(’,’+: P)3,’-+: P):5-’,E KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. M D\ G’*) 5A A:’H0, -\ <(’,’+: 053’Y5(,+: P):5-’,E ?\ <(’,’+: .2))? [I).,’5( 6N ! <(’,’+: P)3,’-+: P):5-’,E ]H3)+,)., ,5 :)+.,\ 9\ 6 = ! = % ^\ % = ! = 6 /\ +:: ,0) .+*) "\ ’*25. .’D:) ,5 ?),)3*’() KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. K A35* ,0) ’(A53*+,’5( H’P)( [I).,’5( 6
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!"#"$%%! ( [I).,’5( 6N ! G’*) 5A R:’H0, ]GQR\ ]H3)+,)., ,5 :)+.,\ 9\ 6 = ! = % ^\ % = ! = 6 /\ +:: ,0) .+*) "\ ’*25. .’D:) ,5 ?),)3*’() KLML!NNK O)-,I3) N1 7 !" $ %" &’()*+,’-. 6N A35* ,0) ’(A53*+,’5( H’P)( [I).,’5( !
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Note4 - !&quot;#&quot;$%! !&quot;#$#%&quot;#&amp;'()*+,'-....

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