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Datenanalyse WS 2001/00 Author(s): Pruys, H. Publication Date: 2001 Permanent Link: https://doi.org/10.3929/ethz-a-004444215
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!#" $ &%$ ' ' ( (0)+/ '* ,1 ' 2-!* '' , ( (' $! -'.+* ', * 3(&( ' !5 // ' 24* / 3 2 13 / 62-. 1 3 / 762-.28* '' ( (' !' -'.+* ', * '3 , (&($ !-/ '. 281 * ' -.+* "( '5 / 3 28* 9G!:$<#;Z[:$<>C< =A!?Q F@4:A!F#BD< CL E!E4G&FHG+G!CL ?JC]I+\JA!? E+@4K8CF^!L E+M$LE < < C`$_A+a ?# G+L L< C]F>G+bHL ?CN:$=#cCE+OOdN:4A!P+E+Q8G&G+CG+?JL RCfE4FeCL ? < S$F :$M4Q @$Q C#?:$TBUVNB]L E+S:$<W4? L XY:4A!E4E+F C$G g Z@4CA+E!_ :$CA+EDCh#?L :$?iQ <;G+L pC#q I!r A+E+K8FL M4EBDL Fij&kml`:$A+_ n4< M]< L E+GG!L C#E8A+BDC?L < oP+CEZ[C< A+Q F:$F C<oP+M4E sv &su( t v ! v %w&(& !/ x2 %v &( )!68yy z)z)|$6 {6 trapezoidal rule
histogram
1
0.8
I = 0.992
0.6
sin(x)
sin(x)
0.8
1
0.6
0.4
0.4
0.2
0.2
0 0
I = 1.004
0 0
=#Q <[EH:4a oP!< F Cg+9#:$OA ^CE8A+F OCEhL ?NG!L C;I+A!E+K8FL M$E $ 0.1
0.2
0.3
x/pi
0.4
0.1
0.2
0.3
x/pi
0.4
!"$#%'&)(*%!+', -'. /10.2243 5 6 . 7 8:9 , $9 ;<7 =>7 " 9 @A B A C D EF A HG A HB EIF B AJ JK A E : LMN/1 } " i:_:0 ~ $7 ;w_ i 2U;H. 7 " `a:; _19;H0.97 /_3 $i f:.9i:.=M7 " 9;H7 _
$7 `a197 0;<"&d;<7 y 01;Hb 7 ;9f:;H. _1i 2U;H.7 " `a ;H_#M9a:;<297 6i:_ f;<"!017 b:9!r:7 ;Hy ;#;9a:/:f:;H_Dedf:7 ;g01;H_ i:;H. ;Uz{;<" i:y 99; y 7 ;H ;H. _1y ">f 7 ;$" 7 2U8 y ;)y 7 _:;<. ;) _19 ;H. 8D/y 97 /_M3 u;0i:9;$z{;<" i:y 99;)y 7 ;H ;H. 9>: }i . y _ 01" 24r. 7 7 ;H. ;H_ f:;U" 9 ;H97 0;h:i _:6197 /1_:;<_=d#M%c&)(d%!+a 9t{;H7'h i _:6197 /_:;<_ Q i:_ f QH : }i .)f 7 ;!_ i 2U;H. 7 " `a:; _19;H0.97 /_*
!#"$ %'& ( )*#,+-(. / 01## 2 / 3 %4& () %4& (=>()A@B%'& () ; 3(65 798: >( C "#DE / +-GF=,H -"IE / 3 %4& () %4& (=5*@ @A>9 BDCE9 F0<G*B !" ##,HI 9 J 69,;50K 7 9,LEJ 67B 9J <9NM09 B @ :;G*7 9 6 O 9 B>9 6 INH @ @ P 456Q@ :;B 9 J 7 9R9J 6Q4SUTWV?SDLYX ZYBG*[*B5 I,I =\>5*@N>J 9] H 6F<J G06Q^U_ `baNced*`fg`h 6 HI 9 BJ @ :;>J i 9 B 9 6j J 9 B M09 B [0K 9 J :;9r>5*@nsk9 @ H K <5< I J 9 BW5*65*K t<J @ :;9 6RVvG*u @ H 6[P 4J J 9 @ 9 Bn@ J Ixw K 9 66 HI 9 B J @ :;96ynJ i 9 B 960< J 5<J G*6 O G*K K 9 6 O J BnJ I 6\5*u :;@ < 96SW7X @ :;6J 9 6 H 6>>J 9r9 60<@ w B 9 :;96>964SYTWV\SDLYX ] H 6F<J G*69 6 }DH 6> ~ z m Y
D\U
kDED
yn9 BxLv5*;6{9 J 69 @NZEK 5069<9 6 HI >J 9G0669RF5*66 I 5*6{5650K t<J @ :;p7 9 B 9:;69 6\zUynJ 9 0<G*u B H 6[09 6x> H B :;x>J 9n5*6>9 B 9 6,ZYK 5*69 < 96NF*5*66 I 5*6n 9 >G0:;,6 H BE6 HI 9 B J @ :;N7 9 B*H u :F0X @ J :;0<J [*96bzYynJ 9mY60< O J :FK H 6[p>9 Bx6 HI 9 B J @:;9645<;9 I 5*< J F O 5*BN96[pM09 B 7 H 6>9 6 I J 9 6 G0B <K 5 H 96>,[09 65 H 9 B O 9 B>9 6>9 6LE9 G*750:;0< H 6[*96RJ 6>9 BWSn@ < BG*6G I J 9*z 6A>J 9 @ 9 I Sn7@ :;6J < < O G*K K 9 6 O J B H 6@U5 H >5*@Y O 9 J F\G*u B w 9 B X ZYBG*7K 9 I 7 9 @ :;B50u 6F*9 6 H 6>>J 9m6 HI 9 BJ @ :;9VvG*u @ H 6[{>9 BRyDJ ib9 B 9 60<J 5*K [0K 9J :; H 6[09 6 I J 9 BR5*65*K t<J @ :;9 6 M09 B [0K 9 J :;96bz E0? R \?? 0 LE9 JQ>9 B 5*65*K t< J @ :;9 6¡LY9 B 9:;6 H 6[ O 9 B>9 6¢>J 9£VEG*u @ H 6[*9 6¢M0G06¢ynJ i 9 B 960<J 50K X ¤ K 9 J :; H 6[*9 6¥[09 @ H :;0<zmLE9 J{>9 B¦6 HI 9 B J @ :;96¥LE9 B 9:;6 H 6[ O 9 B>9 63ynJ i 9 B 96jX ¤ K 9 J :; H 6[*9 6R7 96 H <j<zS H @W>9 BWynJ ib9 B 9 60<J 5*K X ¤ K 9J :; H 6[ `U_ © a `?_ ©\°Q±© aUf{`U_ © a §¨ _ ©aYc ª ©¬« c ®v¯ ±© ª ²³
! "$#&%'" (*),+.-0/ ! "$#1%'%'" +3" 2 / ! " +
4 56 487 ' ':9 ;<6' = '?>@ 5 %,A B C= ED 5 7 * =9*5 F =C @' , = 7 ' 5?C;< 5 4?4 5CG<' 5H;< 7 9* ,5'I$ 7$*J =@ 4 5 K L M 9 4 71! N 9*L 5* 5 + 'E O 9 J 5 @G 5 ;< ' =566 'P / ! "$#&%'" +Q- / ! " +#&%'" ! "$#&%'" (*),+ ! "$#&%'" (,)*+Q-R ,! "321%'" (,)*+$#&%'" S* ! " + B T= 6U L 9* , ;<= ,= * ! V,+ = ! V,+ WG 5 "W-XV ;< 7 9 =,5'I* ;<'55 / 4 9* B 59* 5 = ! %'" (,)*+.-C ! V,+$#&%'" S*! V,+ (*) Y[Z \=]_^,`^ ]a_\=b3]Cc@d ` egfih j 5 Fk:9* e ' 'TlW 9, 5@m' ',5 @7 =T9 T Fk:9, h B * *I$ :7 9, @ B *= ?9 L ' 5[ 4 B ,6 O= 75[ 5 ' =E9, *=,4 4 ':m =$A N * =9 5 'n 9*J 'n [ =I_=9* om9*=@ @ ! /_p q + rW;< ? *5 A 9, N 9*L 5 , 5 5'P S,! " +.-Q2s h t / u
S*v*! "+3-w2s h t q u
4 5 t xW- / x_# q x U 6U L 9* , ;<= ,= *'? 9 J = / ! V,+.-Ct'y pzq ! V+.-XV p ! V,+.-XV p v*! V,+.-X y oW 4 L 5 {* *,;< 'E>E 5 t y 9*J *5 '[{,,@ TU=L 9 =, , , = 7 5 y 9*;$I3*;@ 7 ' rW O ,I_ N ' I3 =?, * :r. O= *I_' '1l39*9*;< ,=6 FK6M O< ;<=9* 5 A k:9,{, , [ 4 ?;< '= 5 oW9, 7 {, 4 56=9 =9, M5 $P t[- } #&~ | *
!" #%( $& ' )+$ * $, '.- )/ 01/ 2 2 3465 &87 ' ) /7 0 /7 ' 9+:. - 7 9+: (;8< = = 1> ?> 2 @= > = BAC" @"1 .; 2 EDF'HGJILKM' N 9+:.-PO )/ I(- 0 / 7 O Q+365 Q D R 'SUW TVV X I 9+: - ; ZY[ 4 34 (\ ] > 0/_^a` Q9+:BO )/ % %D ^cb 2 3 de 4# R ^X ; +; f 1 \ ] > 0 /g ` Q9+:hO ) / % D g b 2 3 fd4 # R giX ; @j81344 %\ kC\ 0 / ' ` Q19+:BO ) / l ; +mf 3 + n\ k\+ oA 1 " 34 2 2 9+:BO ) /7 d4 4 34 2 2 0 / 7 O )/ ] k "p] > 01/ ' ` 9+:BO )/ qLrnsnturv w px@ywz{6yn8| jw " 2 2 }> _\ f34 ek6 n %o \ | 2 ! @=_ _d4 !C n346"> 2 \ P1 ~ ! "C" n 2 2 6l f fxPywz{?yfw| w!C " %8 #8 0 8 # " 2+ # 0C # # 34] " 2 [ !1 n 2 5 8 # 0 8 # ? # 01 ?I(
O Q# X 8 X # 0 8 X # b ? b # 0
O Q # Q 8 Q# 0 8 Q #
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O Q# 8 # 0 8 C# Q
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O Q# l l l l l l l l l l l l 8 # 0 8 # N X #
? N X #
# 01 Q N X #
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! " $#%" !&"'() (%* (",+ -." / 021 34 * + $5" -.67" 879$9 " !$: ;=>@7@ACB7D$< @E @7F7GH I*JKML N O L $ L .P L 7 L $ L .P L 7 K QR K L S P L S*7 M K S T L L L L L L U O Planetenbahn (+++ numerisch, --- analytisch) 1.5
1 + + + + +++ + ++ +++ ++ + + ++ + ++ + ++ + ++ ++ + ++ + ++ ++ + + + + + + + ++ ++ + + + + ++ + ++ + + ++ + ++ ++ + + + + + + + + + + + ++
y
0.5
0
-0.5
-1
-1.5 -1.5
-1
-0.5
0 x
V W
0.5
1
1.5
m << M vy0 = 0.55 E = -0.52 eps = -0.55
Einheiten: G*M = 1
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