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classical mechanics lecture notes, Lecture notes of Physics

lecture notes by Prof. J J Binney with solved examples

Typology: Lecture notes

2018/2019

Uploaded on 08/20/2019

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E2 f B 7 F:,D4F.F?59E'@hg0WiNM jklQR,NMhS>U,R,V#NW1Qnm1R*OpoqrBs0UM NklQnt%QnkljYNWiuwvhm1NW1klmxyS>Uz R,V#NW1QR*O*@ f={ +2| EA8:B B AFE':B :C :9@A1,/;DEC}~/?57>ED. .KFD= .F9@A17 9E'C:=@?B/?A !F. :E D:;F.F91+/?5:8= .K5,@E :D#E ?5.K5B/+D:'0 .K591+ E/7 C:5B>A/7 9#!25.F,;F.K5,= .FB B :'!F: B 7 D5,@A1,/;#€ 2 a 2i| ,/95.FB/+ @)S>NkeV#UxENklQR,NMS>UkeV#q%uPOEqopS>U,R,V#NW1QR*O*@)X(5,/7 9#!F:,%? AE5957/$5:B ; 7 9E 7 !F? 0e5B D. .KFBD#‚/. . E .K(5?57>E/7>=A/:%+ 0 .F,C . E‚591+ :,C!F,@AK+A/:E2       C     *5   6 .0 7 A 0  AS 0 ;IS1@ E . AS ISW 7+ +/S; 0  [XHA191+ [  ] \.^T +/S IS  ' + +/S - 0  [1# 7[F2 L; I : 95::%+>/.(C 7 957 C 7 `: [ W 7S; X'0 ,/.FC 7[F2 L;=A7 /? ,/:E](:=*./.6/?5:E(A/? 7S; 2I :DCDA;>E : /?5:BT f :%$ 9 7[F2 JK;T(5,/. 7/+ :%+A8:%CDA"F :=/?5: E]#DE/7 C/7 .F9E 1S !  ' ! + +/S !S -  [ IS  ' + +/S - 0  ["# 7[F2 "; X 7 9= :3+ . :E 95."0+ :'(:91+ .F9' )@/?5: .K(/7 CDA1B (A/?(E/A/7>E-:E K ++/S + +/S S  7+ +/S; 0  ["! ! A?57>=@? 7 C (5B 7 :E 7S; ^] \T  # S[ 4 # S +/S ! 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A,/7 ]/:9 7 9 /:,/CDE .10/?5:.(5,/7 C :%+ = . .F, + 7 9A/:E/?5:.F 2 :F2 7>E =  .0 ! 0  .0 #"" A @ $  @ "" 0 .0  c A @ c 0  A @ d7%  @ ;B .0  c   @ c 0 7[F2 [IK; G ?5:.(2 :F2 7>Ee E >B7  @b!]; E . 5  .0  c A @ c 0  A @ d7%  @ ;$ .0  c   @ c 0 4 >I# 7[F2 [%d;a 96A,/7 /7 9#!E+ .A9/?5:pT f :%$ 9EA8: ,/:=A1B B /?A A @ d7%  @n;I  @ dK7 A @ !.; 2cI :/?5:9 -91+ K ++ ( 5( A @ 4 ( 5(  @ ++ 7% A @ !  @ ; 4 8  A @ !6 ((  @ ' .0  c   @ c 0 4 >5-:# 7[F2 [*<; b'.FB B :=*/7 9#! :'F:,/;/?57 9#!:/.K!F:/?5:,‚A8:%?APF:=-9A1B B ;   @ I& A @ ! 4 ( > ('(  @ A?5:,/: > ('[ > 4 .0  c   @ c 0 # 7[F2 [JK; a 9A ,/."@A/7 9#! 0 ,@A1C :c/?5:,/:87>EA = .F9/,/7 D#/7 .F9/.0/?5:*)/AF== :B :,@A/7 .F9,+  @ 0 ,/.FC /?5:.-    F;  *K I&!/ A @ @1A191+ /?5:0(."/:9/7>A1B 95::%+5Ec/.:D:%A"#!FC :9/:%+ D ;DA./:,/C /?A!F7 F:E-,/7>E :5/.p/?5: *K   );  & # I;  *K 10 0 4 7% d  @n; 25.F,@= :EE]=@? 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A1B B.10h7 :! ! )i;E 7 C:5B @A195:.KE B ;D7>E +! 0  c        c 0  H 0 ]H 0 ]H 0 0 7H ; 0 7E 7 95? 0 = . E 0 5 = . E ? 0 E 7 9 0 ; 7H ; 0 7= . E ? 0 E 7 9 0 5 E 7 95? 0 = . E 0 ;$ 7H.)i; 0 = . E ? 0 = . E 0  0#" 7= . E ? 0 4 = . E 0 ;W 7H ; 0  7H ; 0 X = . E ? 0 = . E 0 i7H.)i; 0$ # 7[F2 [ P; ^ 7  7/+ 7 9#! /?5,/.K#!F?9D ;+ 0 A8:!F:‚/?5:.F 7 95:/7>= :95:,C!F; 7 9 /:,/CDE .10‚7 A ! A Y! A)i;*? =  .0  ' +! + - 0  .0  0" 7= . E ? 0 4 = . E 0 ;W A 0  A 0 X = . E ? 0 = . E 0 A) 0#$ # 7[F2 I1K; G ?5: :%$ 9E .10C ."/7 .F9(A1,/:0/?5:,/: 0 .F,/:  0% ++ 7]7= . E ? 0 4 = . E 0 ; A 4 .0 E 7 95? I % A 0  A 0  = . E 0 A) 0'& )( >( K  0 % ++ 7]7= . E ? 0 4 = . E 0 ; A 4 .0 E 7 9 I& % A 0  A 0 4 = . E ? 0 A) 0' &  ( >( K  0 0 ++ % = . E ? 0 = . E 0 A) ' 3 )( >( ) K # J K ' LT &  5 &  5 ;   &  '  )( HA"!F,@A19#!F7>A19 + ; 9A1C 7>=E,/:A1B B ; = .FC :E7 9/. 7 @E-.A9 0 .F,/?5:0+ ; 9A1C 7>=E-.10A ,/7 !F7/+ D.+ ;p:/?A87>E'A19D.KD 3:=*8E]=@? AFE8A E](A19595:,T/?A= .F9@A17 9E8Ap AFE 95C:D:, $ .10)(A1,]/7>= B :E/?AA1,/: E . E/,/.F9#!FB ; = .K#(5B :%+E/. :AF=@? ."/?5:,T/?A A8: CDA; = .F9E 7/+ :,/?5:‚+ 7>E@A19= :ED:A8::9p/?5:C /.D:-  :%+ 2a 9:/?57>E-A"(#(5,/./ 7 CDA/7 .F9 @%/?5:= . .F, + 7 9A/:E.10:'F:,/; (A1,]/7>= B :A1,/:.F 95.A9*AFE E . .F9(AFE5A8: ?APF:p+ :/:,/C 7 95:%+6/?5: E 7 6!F:95:,@A1B 7 `:%+ = . .F, + 7 9A/:Eh/?A%A1,/: ,/:%$57 ,/:%+/. ( * l `Fc,+ `.-2hji/?d f`c-10 0 m2+ac      AFE  . A191+  0F2TX . B :%4 E =@?5. . E :  .5/.ED:/?5: A 7>EA"D.K‚A?57>=@?6A8:%,/."@A/:%+B/?5,/.K#!F?65B :, A19#!FB : $ 2-G ?5:9 A$ = .F9/,/7 D#/:E A$  .0/.  25| 9(7 9= ,/:C :9 7 9 )*,/."@A/:Eh/?5: E ; E/:C A"D.K H 2 G ?57>E B 7 :E 7 96/?5: (5B>A195: .10  0A191+  2DA191+*7>E 7 9= B 7 95:%+ A A19#!FB : $ /.  212E< :9= : A) = .F9/,/7 D#/:E A)7= . 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E :=A8: = .K5B/+ -91+ $ = .F9E@A19@E-.10HC ."/7 .F9 .!###!  2c| 91+ E]#(#(. E : 7 hA8:,/:0(. E/E 7 D5B :5/.p-91+ A E ; E/:C .10=A195.F957>=A1B= . .F, + 7 9A/:E7 L ! B;E]=@?9/?A : e  :@=128G ?5:9 /?5: :%$A/7 .F9E .10C ."/7 .F9 0 .F,‚/?5: 4 E‚A8.K5B/+ D:/,/7  7>A1Bl@ K A : : W : ! 'X  4 ( (  # 7 I 2 < <;A191+BA8.K5B/++ :C .F9E/,@A/:5/?A Y7 L ;TA8.K5B/+BD: 7 91+ :'(:91+ :9.10 /?5:  4 E2G ?57>E8B>AFE .KDE :,C A/7 .F9BA8.K5B/+ A1B B .AEh/.DE .FB F:0/?5: :%$A/7 .F9E .10C ."/7 .F9 0 .F,h/?5:  4 E'?cA8:A8.K5B/+ ?APF:A   ( ( : [ 0 E! A = .F9E@A19   ]7];   C7K;B 0  # 7 I 2 < JK; X . :'F:,/;/?57 9#!BA8.K5B/+ B 7 : A .K5, 0 :: 7 0A8: = .K5B/+9-91+@$ = .F9E@A19@E .10c/?5:C ."/7 .F9*A191+*= .K5B/+ :C:D:%+6/?5:E : AFET/?5:7N C .FC :9@A#4 .10A E ; E/:C .10=A195.F957>=A1B = . .F, + 7 9A/:E2 0 G ?5:%CDA"!F7>= = . .F, + 7 9A/:E L [ A191+A1,/:%=A1B B :%+ *  BK, 5 &  = . .F, + 7 9A/:E'@/?5: 14 E‚D:7 9#! /?5: AF=*/7 .F9E A191+/?5:  4 E/?5: A19#!FB :E2( * l `Fc,+ `.-2hji/?d f`c-10 0 m2+ac( * l `Fc,+ `.-2hji/?d f`c-10 0 m2+ac0$hMd l gF` d fmdd h + `Bm2+0 `Cd h`  + ` /"d f` cmMcmAc `;dh  h  `Fi2d m  `  `  al  `   aig;d l hjicc md l c - l i ed fl cgFhji/l d l hjim  `c mMl /Dd h+ `"! l il i2k2h 0 a d l hji# v "    B     !   : G‚7  !%> ;D:‚/?5:‚!F:95:,@A/7 9#! 0e59=*/7 .F9D.10i/?5:h/,@A19E30 .F,/CDA/7 .F98D:A8::9D,/:'!K5B>A1,= . .F, + 7 9A/:E‚7 !%> ;-A191+ AF=*/7 .F9 A19#!FB :D= . .F, + 7 9A/:E2 G ?5:9YA8: =A19 E :E/?57>E./.*:B 7 C 7 9A/:  ( G  ( > 0 ,/.FC  @:(5,/:E/E 7 9#! AFEA0e59=*/7 .F9 .10‚7  !%> ;*? Y7  !%> ; [  ' ( G( > !%> - # 7 I 2 < L; 68; C . 7 9#! .F9 A19D.F,CD57 TA8: =A19E A1,/;:/?5:V )(5,/:]3; C:=@? AA7 B B A?57 B : ?5.FB/+ 7 9#! = .F9E@A19c/?5:  2c| ETA8:5 A1,/; /?5:= 7 9/?57>EhA A;  C:E,/:CDA17 9 = .F9E@A19A/?5:%:95:,C!F;  .10 /?5:%.F,CD57  7 96$5:E/7 .F92G ?57>EE]#!K!F:E@E/?A A8:%7 9F:E/7 ! A/:0/?5: 95.F9 B 7 95:A1,‚(A1,]/7>A1B + 7 } :,/:9/7>A1B :%$A/7 .F9  ' ( G( > !%> -  !   9  BK  * 1 ->    # 7 I 2 <"; a 0A8: =A19 E .FB F:p/?57>E :%$A/7 .F9 @ A8: 7/+ :9/7 0 ;6/?5:DA1,CD57 /,@A1,/; = .F9E@A19@E .F9>A?57>=@?3/?5: E .FB /7 .F9?G‚7)> ;=+ :'(:91+5E A7 /? 0e59=*/7 .F9E'.10 /?5: = .F9E@A19@E-.10C ."/7 .F9  2c5.F,8:5A1C (5B :K@K/?5:=<F 4:%$ 9D0 .F,8A 0 ,/::5(A1,]/7>= B : C . 7 9#! 7 9EA8. + 7 C :9E 7 .F9E 7>E c  G c 0 I&   7 I 2 <\; I :.A,/7 /:DG‚7R); ^G  7 i;e G  7R#; A191+ E .FB F:E7 I 2 <\;D ; E :'(A1,@A/7 .F9 .10 A1,/7>A"D5B :E'? = .F9E@A19 [   ' ( G( - 0  I&  4 ' ( G( R - 0 [  # 7 I 2 <QP; G ?57>E:5A1C (5B : 7>EF:,/;@A1C :K@"D#c/?5:/:=@?5957/$5:hA8.F,CF EA1B>E . 0 .F,C .F,/: = .FC (5B 7>=A/:%+8< A1C 7 B /.F957>A19E)/?A'=A19595." D: E .FB F:%+D ; ."/?5:,C :A19E2 G ?5: E 7 C 7 B>A1,/7 3;ED:A8::9/?5:.<F 4 :%$ 9 A191+E/?5:/7 C : 7 91+ :'(:91+ :90X =@?5,/.+ 7 9#!F:, :%$ 9 7>E .KD 7 .KE2I : =A19 + :,/7 F: /?5:E<F 4 :%$ 9*0 ,/.FC < AFE 0 .FB B .A E2:5.F, E 7 C (5B 7>= 7 3;3A8: = .F9E 7/+ :,0/?5:DE](:= 7>A1B-=AFE :.10 A(A1,]/7>= B : /?A C .F:E 7 9 A(."/:9/7>A1B:>E7R); 2:a 0T/?5: (A1,]/7>= B :?AFE=A8:B B  + :-95:%+*:95:,C!F;K@ 7 @EA APF: 0e59=*/7 .F9 =7R); C:E E/A/7>E30 ; /?5:./7 C : 7 91+ :'(:91+ :9.X =@?5,/.+ 7 9#!F:,:%$ 9       7  0 1I& &>:;  2hI 7 /?5.K B . E/E.10!F:95:,@A1B 7 3;K@#A8:=A19 A,/7 /: ":   @#A?5:,/:DG‚7R);87>E A8(. E/E 7 D5B ; = .FC (5B : 0e59=*/7 .F9(.10:R2'G ?5:9  0   4  0 Qd  :   7 G !  :   % c  G c 0 4 7  0 G ' # 7 I 2 J1K; X 7 9= : A8: A1,/:8+ :A1B 7 9#!9A7 /? = B>AFE/E 7>=A1BC :=@?A1957>=E'@ A8: A1,/:7 9/:,/:E/:%+ 7 93/?5: B 7 C 7    K52G ?5:9>/?5:DE := .F91+ /:,/C 7 9/?5:.D5,@AF=,F :‚ A1957>E ?5:EA191+B/?5: Gha]X D:= .FC :E K  0 I&  >  4    :    c  G c 0 I&  > 4  ! ! 7 I 2 J[P; A?57>=@? 7>E E:   /7 C :ET/?5:.<F 4 :%$ 92G ?57>E‚+ :,/7  A/7 .F9 ,/:'F:A1B>E/?A/?5:!F:95:,@A/7 9#! 0e59=*/7 .F9 .10 /?5:0/,@A19E  0 .F,/CDA/7 .F9 0 ,/.FC .F, + 7 9A1,/;:/. AF=*/7 .F9 A19#!FB : = . .F, + 7 9A/:E-7>E  /7 C :ET/?5:0(5?AFE : .10 /?5:=(A1,]/7>= B :K4 EA APF: 0e59=*/7 .F92 I ?5:9 .F95:5(AFE/E :E0 ,/.FC A APF: .K(/7>=Ec/.:!F:.FC :/,/7>=A1B.K(/7>=E'@ ;F.K 95:'!FB :=* A/:,/C :%$57  A1B :9T/.p/?A‚+ ,/.K(#(:%+ 0 ,/.FC 7 I 2 J1K; 29^ ,/.K(#(57 9#!6/?57>E./:,/C 7>E =A1B B :%+ CDA"F 7 9#!6/?5: eH # p    R )9Y   2 G ?5: A"(#(5,/./ 7 CDA/7 .F9 7>E!F. .+wA?5:9CDA19 ; A APF:B :'!"/?E A1,/: = .F9@A17 95:%+wA7 /?57 9 /?5: E CDA1B B :E B :9#!"/? A7 /?57 9 A?57>=@?  G =@?A19#!F:E A"(#(5,/:= 7>A"D5B ;F2 /fK  L  #  K,  *K3  :9   ( f 0n/:9 @-0 .F, :5A1C (5B :9A?5:9 + .F7 9#! E@A/7>E/7>=A1B C :=@?A1957>=E'@.F95: 95::%+5E A = ,/:%+ 7 D5B :9+ :-957 /7 .F9 .10 N (5?AFE : E](AF= : F.FB 5C :K4 2Ya 0 .F95: 7>E8E 7 9#!Yb8A1,]/:E 7>A19 = . .F, + 7 9A/:Ep/. + :E/= ,/7 D: A E ; E/:C .10 (A1,]/7>= B :E.10 CDAFE/E*' ]@'7  7>E 9AC5,@A1B/.@A"F :h/?5:‚F.FB 5C ::B :C :9c/. D:0+ [  7% 2 + 2 R\ l+ 2 \ ; 26-7 '7>E 9 4 -7 C C :%+ 7>A/:B ; .KD 7 .KEA?A /.E : 0 .F,+ [ 7 9 A C .F,/:= .FC (5B :*=AFE :F20a 93(A1,]/7>=5B>A1,%@7 0-.F95:8+ := 7/+ :%+~/.9+ :E/= ,/7 D:p/?5: E ; E/:C .10(A1,]/7>= B :E ( * l `Fc,+ `.-2hji/?d f`c-10 0 m2+ac    A    Y?2   ;/  2 M 6%(  ( L !   ( 0 G(  ( L @E . W  E!  Xf   (  (  !   ( (   !   (  ( : !  4  (  ( !  (  ( : 4 (  (  ( 0 G( : ( 4 ( 0 G( ( : K # 7ea]a 2 JK; 3     R   9    " ;  /fK0/ / ;   9   * H   &   ->    I : E@A1,]TD ;:-91+ 7 9#!./?5: A1C (5B 7 C1+ : # .E0‚/.:!F:-0 ,/.FC 7%.!%>.;/.7E0"!%>f0%;*@A?5:,/:‚/?5: 7 9/:,C A1B E0 4 %.87>E8E CDA1B B 2a 9~^ 7 ,@AF="4 E 95."@A/7 .F9 @/?57>E A1C (5B 7 C1+ : 7>E # .E0V)>f0 c V!E0 ! 7ea]a]a 2 [P; A?5:,/: c V!E07>E0/?5: F : 7 9/.A?57>=@? c >. ?AFE :'F.FB F:%+(A E012=a 9*."/?5:,=A8.F, +5E'@ c V!E07>E0/?5: E .FB /7 .F9*.10c/?5: /7 C : + :'(:91+ :9=X =@?5,/.+ 7 9#!F:, :%$A/7 .F9 7  #;80 .F,7 957 /7>A1BH= .F91+ 7 /7 .F9 c V!%.  c >. 2-G ?57>E7>E c V!E0I :    _` _ba   c >. # 7ea]a]a 2 IK; < :,/:c/?5:-:(.F95:9/7>A1B17>E /?5:-.K(:,@A/.F, A7 /?./?5:'E/A1C ::7 !F:9 F :@E c   AFE /?5:T< A1C 7 B /.F957>A19  @ A191+%:7 !F:9 A1B 5:E:%$A1Bi/.D:    _` _ba   @A?5:,/:=/?5:  A1,/:0/?5: :7 !F:9  A1B 5:E8.10  2-G ?A7>E'@ :    _` _ba   [ c   :    _` _ba     c # 7ea]a]a 2 d; 7GH.9(5,/.F:./?AE7ea]a]a 2 IK; E/A/7>E-:E5/?5: i@- E E]#DE/7 C/:~7ea]a]a 2 d; 7 9/. 7ea]a]a 2 IK; A191+3+ 7 } :,/:9/7>A/:8A 2 ,2 2YE012 ; f 5, A1C (5B 7 C1+ : =A19 95.A D:.A,/7 ]/:9# .E0 )>f0 c :    _` _ba   c >. ^] + 2 )>f0 c  c :   _` _ba   c >. ! 7ea]a]a 2 <; A?5:,/:.E : ?AFE‚D::9(CDAK+ : .10/?5:%0AF=*5/?A8+ 2 c  c 7>E8 E5/?5: 7/+ :9/7 3; .K(:,@A/.F, E 7 9= :/?5:E@A/:E c  .10A8:B B  + :-95:%+ C .FC :9C5C0 .F,/C A = .FC (5B :/: E :2 A191+>/?E./?5:D0e59=*/7 .F9 .107  A"(#(:A1,/7 9#! 7 9 7ea]a]a 2 <;%7>EA 0e59=*/7 .F9 .10h/?5: .K(:,@A/.F,@E  A191+ >26 :%4 E AFE/E]5C :=/?A :'F:,/;  ?AFE‚D::96(. E 7 /7 .F95:%+/.8/?5: B : 0n .10:'F:,/; >2'G ?5:9 :'F:,/;  =A196D: = .F9E 7/+ :,/:%+B/. AF=* /./?5: B : 0n8A191+ D:,/:'(5B>AF= :%+8D ;7 @E-:7 !F:9  A1B 5: @A?57 B ::'F:,/; > AF=*@E-E 7 C 7 B>A1,/B ;p/./?5: ,/7 !F?2cX ./?5: = .FC (5B : 95C:D:, c :   _` _ba   c >.D:= .FC :EE 7 C (5B ; :    _` _ba    c >.I :    _` _ba   :    a 7 I   ; 2%0 ! 7ea]a]a 2 JK; A?5:,/:  7>E/?5: = B>AFE/E 7>=A1Bc< A1C 7 B /.F957>A19 :' A1B A/:%+ A./?5: = B>AFE/E 7>=A1Bc(5?AFE : E](AF= :8(.F7 97 !%> ; A191+ A8:D?APF: E :%+ /?5: 0AF=*T/?A c >.-7>E\ ET/?5:%= .FC (5B : = .F9 #! A/: .10 /?5:=A APF: 0e59=*/7 .F9 .10HAp(A1,]/7>= B : .10 A8:B B  + :-95:%+ C .FC :9C5C 2cI ?5:9 A8: 7 9E :,]p7ea]a]a 2 JK;'7 9/.~7ea]a]a 2 <;8A191+ E 7 C 7 B>A1,/B ; ,/:'(5B>AF= :)>f0 c TD ; A:(5B>A195:=A APF:K@A8:0-91+ # .E0  [  2 ] + 2 :( 8 7  ' dK7)>f0 4 >.; 4 Y7E0 4 %.;F-:# 7ea]a]a 2 L; T$A/7 .F9Y7ea]a]a 2 L; 0 .F,5/?5: A1C (5B 7 C1+ : /.!F: 0 ,/.FC .F95::'F:90/. 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A7/+ :B ; E :'(A1,@A/:%+ :'F:9@E7b!%> e;8A191+ 7 !%>C;*@#A8:%:(5,/:E/ET/?5:A1C (5B 7 C1+ :/.E(AFE/ED:A8::9 /?5:CD ; A (A1,]/7>=5B>A1,h(A/?>   >.  ###  > AFE/?5:.(5,/.+=*#  . # .E04Sddd  #  7ea]a]a 2 ";C; .10JA1C (5B 7 C1+ :E-.10 /?5:0 .F,/C 7ea]a]a 2 L;.F:,-E CDA1B B7 9/:,C A1B>E57 .! ; 2I :5/?5:9D.KD@A17 9 /?5: A1C (5B 7 C1+ :‚/.p(AFE/ED:A8::937 !%> n;-A191+~7!%>];cD ;~NW1j:(A/?BD ; E]5C C 7 9#!97ea]a]a 2 ";.F:,-A1B B  A1B 5:E-.10i/?5: 7 9/:,/C :%+ 7>A/:5(. E 7 /7 .F9E> 2-G ?5:-9A1BA1C (5B 7 C1+ : 7>E #   B 7 C  [ 2 ] 7+ 2 + 2 > ;8:( 8 7   '  dK7)>   . 4 > "; 4 Y7   . 4  ;F-: = .F9E@A19 @] > :( 8 7  ] ' d'+ > 4  +F-:# 7ea]a]a 2 \; < :,/:/?5:E ; C:D.FB > C :A19E.F95:87>E/. 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