! "# $&%'(&%)+* ,-/.&-10+2436587 9 :<;>=?:<;>@BA6CD=FE&=HGIGI=HJ6CDAK=HLNMO;>=QPRL6J ST;UJ VJKW XYAZV [\VKM^]+M`_aGcd b MOVJKe W=HfgXYh;IM d GIijVKf$CD=\M`fk;IJml d G don ;>=HJp qsrtDuDv'wxvyzx{'tDuD|/}x~uDrqs) r`{uDr'vr!{'{|/cr${'/}xvyzxv'cr!$wczUrD}U8}IwcTcr)D|/YD 88}Uwxc )rD}xzxcz6|/~uD}Iwz{{' uDr)cr'U{' w1{'>'`{'D|/6czIw|)rDyDczR8wxczUrDu\{' )Dy|r tD|/z{'/ D}Iwcz¡D|/D¢w¤£$¥ar$wxczRqs}Uwxzxvr)vr¦u`{w6}\§x{'uDzU¨cuDr©wc{'rDyYªK|}U«$D}x}U|vrDr¬`{'zD ¡Bcz yyc¡BcrRvz{)D|/®`vzU D|}xztD|/z{'/y©{'{|cr¯¨cDzD ~«$¨c)D u)zxcr|/}Uw¤£Z°1|/rD±)cz+¨Dz °1zx«$²{ zxDrDyvzUyc}U~uD{'y'crDr³u)cvzU|cr|}Uw´D|ªK|~u©wxRc/cr©wu)cvzU|'£Hµ²m®Ov'yrDDcr}xv/ |r {'/ycTc|/r$'czU}Uw { rDD|/~uDczo®`vzx D ¡Bcz1|rD|/y6|r)4{'~u)¶¦{wuD¦{wx|}U~uD¶®`v/yczUDrDyr·{'D} D|/c}xzZ³uDcvzU|¡BczU|~u©w¢wYRczUDcr£ ªK|zUw|/DrDy+)cz$wczUrD¦|/r|rDz t)|z{y©{'{| «{'r)r&|¸Rc}Ucr©w/|~uDr¹|r|rDr&«$º y/Uv zU|/ycrqYr$wxc|/F|¼»r$wxzxD½)czs{'{|K)rD+|/r|rDr¾O{~uDcr¿8~uDc|/¡Àr`{'r©w|\¨czIº y'w6zxDr£8µ²^~uDc|/¡Àr`{'r©w|B}x|/cu©w6{'r·`{'}¶tD|/z{'/ D}Uwxcz£©¥Yr©wz6Dr¬®`vzUrD|/c}Ucz tD|/z{'/ D}IwczuDzxzx}U~u©wy'zxvTK|/c/4{/w¤£ªK|8tD|zx{'{'zU·«Àv rDr)cr}xvÁRvuD¶rDyÂy¢ZDrDDr {'/}6{')~u¦6|/w6y©v' ÃÀrD¢w6}Uc|r£)Ä6|À{'rD~u)cr!t)|z{y©{'{|rDrĶ{'/«'cr)}xtD|/z{'/cr$}x|/rD¦)| 8wxczxr) |Å»r$wxzxD¼|/rÂDczs®`vzx½|rD}Ķ{'/«'cr)}YzUwxc|w¤À{'r+)c}x}UcrÆ°1rDDrÆtD|zx{'{zxT {'rD}Uwx¨ccr£`°1|rDK³8tÀrDc|/r©wc|/Dr)yu`{wDz{'TczU|«{'rD|/}x~uDYqs}Uwxzxvr)vÇ°1)Z|/r!ÈYD¡)¡D{)º y}Uww¤\D|T|rÄ6|/¯É}x~uD¦{wx|}U~u¹`{'zxy'c}Uwxc//w|}Uwc£oªK|/·c|r)¨cc/rDcr¹³8tÀr&6zxDr|w Dr|/ÊÄ6|/!{'rDy'cy¡ÀrDcr+Ëv' ¡D|rD{w|/vrDcrvr+Ä6D~uD}Iw{'¡BcrDrD+»{'uDr!¡À¨cc|/~uDrD¢w¤£ µ²r¦{'r)~uDcr¯{{|r&{) crÌtD|/z{'{'zxT¦)Dzx~uÌD|y©{rD¨c~uD|¡B!DrDZ|rDDrÌ}U|~u c|/rDc|/rDu`{'/¡D{'DÇDcr+Ëzxr£Oª{}s8tD|zx{' )}Uwz«{'rDr{'}UvTr)|~u©waDDzx~u+¨c)U{' /|/yKªK|/~uº w}x~u©6{'rD«$DrDyrkcr©w}Iw{'r)DcrÌ}xc|/r1}xv'rDDczUr¯ )Æ)Dzx~uc|/rDcryv'¡`{'rc~uD{'rD|}U D} czU¨cDy'w!6v'zxDr}Uc|r¶Dcz!D|/Ây©{'r)¨c±{{|D·4{''w¤£RqsD~uÍ«{'rDrg`{'}8tD|zx{' )}Uwz rD|/~u$wZ)Dzx~u!D|Ãzxcr©wx|c/sÎav'w{w|/vr¬|/rDcza~u)c|¡Bcr©wx}Uw{rDDcr}x|r6|}U|~u!`{'rDr)| É tD|/z{'{'zxTKr`{~uRcrD|/ycr+Îav'w{w|/vrDr{rDycrÆ) 'wr`DrD¦{'r!`{uDczs{{|r!|w TcuDzv8DczR6rD|yza{'rDycywcrt)|z{{'zUr¦¡Bwzx{'~u©wr+ D 'w6{'}ZrD|~u©waDzZ®B{B|}Uwc£ qs/}xv )D{'}NtD|/z{'/ D}Uwxcz ) ¡ÀzN|rD|/y¥aDzUcu$DrDy'crTDczN{'{Ï)|/6«vrD}Uw{'r©w6}Uc|/r£OÐѪK|/ |/~uD}Iwz{Dzxu©wY}U|~u|r!w²6{ɤÒÒT|/|v'rDcr¬Ó{'uDzxr+DÇ}x|~u!}Uc¡)}Uw¤£ÕÔ ØÖ ×ÕÙ ÚÛ ªK|1u)c)wxRDv'|/rD|zxcr)D1³uDcv'zx|¨Dzo°1zU«8Ü{' zx)rDyY)c}otD|zx{'´D}Uwxczx}F|/}UwHD|/RªK|/~u©wRc/rº wu)cvzU|'$D|/s|/r¦Dr¬}x~uD¨c|/yczZÓ{uDzxr¬DDzU~uqszx¡Bc|wr¦DzZ+{wxuDc{w|/«'z¶Ýs£)Ýs£DÞF|rTDrD È£©u$T'vß+{}x}{~u8)}xwUw}¶µ²r)}Uw|w)wxv'B³Ø~uDrDv/vy'}Iw{'zU«'rqY)àwzU|c¡·zxuD|/c/wc£'qYD}U D u)zIº |/~u|/}UwD|}x¬³uDvzx|/¦|/rkáâÉäãÏå6`{zxy}Uww¤£Hª{'r`{'~u|}Uw`{'}tD|zx{'´D}Uwxczc|/rD¦}U|~u¹| æ {'}x}Uczx}Iwv'ÃÀy©{'}Dz{'{|´{'D}x¡)zxc|wrDDTªK|~u©w¢6/')|DDzU~u±D{'}»D}{'TTcrD}UtD| T|/wRDcÊzx{Á8|w{wx|vrD}I c/¦DzZ{{|acr©wx}Uwu©w¤£OªK|}xªK|/~u©wRc/sZ|/zx¬}U|~u©w¡D{'zc)Rc|/ }x|/}xtD|/z{'Uv zxT|y'¬8wxv'Rc/cr¹r©wu\{' w¤ç)|¡Bc|¶Dz·qsD}U¡Dzx|/w)rDy¿`{'}{}DDzx~u)c|rD{'rº DzUZ|zU¡ÀrDrDÆ}xvT|/wu)|r©wz)cr8wv6r¿|rDuDv'vy'cr{'~uDcr£Fqsr¿|/c/cr±8w/cr zxD|/~u©wwY}x|/~uD{'}Y{'}D{'rDrDr©wczaDza|yrDcr+z{¤8|/w{w|v'rD}x«$z{àw¶6|/wxczZ¨c+8wzxrDr£ K|/c/1D|}xczo8wxczxr)R}U|rD}xvYzx|}x|/ya)rDD{'|w\}xvauDc/è¤D{'Y}U|N¡Àzx|/w}\r`{~u´w²6{ɤÒs|//|vº rDrÓ{'uDzUcr¬|/uDzxr¦y}{'wcr æ {}x}xzx}Iwv'ÃBvzUz{wRzx¡Dzx{'rDr©wu`{'¡BcrDrD¦Z|/cDzRzxÜv }x~uDr£ æ c|ND|/!8wv''6/¦|rD|}xcé»c|wz{Dêczx}Iw·DQc|r) æ |rD«c/yz{')¦vzx{'rDy}x~uDzU|/wUwcr |}Iw¤F¨c|~u)rDw}x|/~u±uD|/r©wczDz´$wv'Rc/·c|/r±u)c/czt)|z{{'zU?{'¡£HtD|zx{'{zxT ¡À}UwxcuDr ã {'/}xv¦r)|~u©wK|/Tcza{'D}YDcr}Uc/¡Àr¿8wzxrDr}U|´y'cuDrÂDDzU~uD| 8wzxrD )rDDDzU~u`{'} {'}uD|r)DDzx~u£ ËDzx¨¨D}{TcrDy'4{''w|/}UwDz1¦{wuD¦{wx|}U~uDZÄ6c|wzx{'yKvrÞF|rDr)¬u$· vy'crDDzc멪K|/ «$Dy{'zIw|y'ËvtBvrDr©w|}IwuDvTvyrÆ)rD±¡Bc|r)¾DD'wD|T8~uDc|/¡À·r$DzDDzU~u`{'}zUvº w{w|v'rD}x}ITTwzU|}U~uDz{¤8|/w{w|v'rD}U £ÞF|rDrD+u$!}UwxDD|zxr`{uDczr$DzZD|/~uD|¡B'£ æ c|6`{'}tD|/z{'/ D}Uwxcz )Dzx~uÌc|r)8wv6zx¨cDy'w·Z|/zx1D|/}x|/~u|/ æ {'}x}UczU}UwvÃBº y©{'}ZDzY~uDc|/¡À{'D}U¡Dzx|/wxw¤`}UtD|/wZ`{}K{'}c|/rD6}xr$wx|/~uD ÎZv/K¡Bc|FDzs°1r©w}Iwcu$Dr)y D}tD|/z{'/ D}UwxczU}c£Bqs}Yc|/r)4{'~uD}v)c\ìD zYD| ~uDc|/¡À´rDcuDTcrÆÞF|rDrDÆu$¿`{'u)cz c|/rD+~uDc|/¡À+{'D}T|}Ucr©wzUvtÀ {'}£NªKcz{}{'r©w|Z|rDz~uD|¡B|/}Uw}xuDz¦}Iw{'zU«¨Dz y©{'{'«©w|/}x~uDr°1¡BcrDuD|/r!«'vrD¨cr©wzU|zUw¤ëOªK|/{'}x}U~uDc|/¡Àu`{wZy'cvTwxzx|}U~uDí1zxvtBvzUwx|vr)cr {' uDr)|~uTc|/rDcz6ío{'t)tD}x~uD|¡B'£)ª{'uDczR|}Iw6}6}x|/rDr©v/è©`{}¶í1zxv¡)c^{'/}R¡ÀrDc})¨¢6|D|/rº }x|/vr`{'/c}aí1zxv¡)c½¨Â¡Bwzx{'~u©wr£F|/|r)¤{'zU|}x|/czUcr!r$DrÂD|/¡ÀrDcru©8Dzxv8)8r`{'T|}U~uDcr c|/~u$DrDyr)rD}xD~uDr(ÞNv }UDrDyr1D|¦¨cc|w/|~u{'r©6{'~uD}xr£RªK|¦µ²)c!uD|r©wxczD|/c}x RvuD¡Bc«{'r)r$wxcrvzxyuDcr|}Iw¤``{T)||/rD¤{'zUcrc|/~u$DrDyrD|/{}x}Uwxz v ´DrDyT|ÇqYº yr8¡)|~«Dc}T°1r©w}UwxcuDrD}¬|rDzTtD|zx{'/Rc/¬y')w·¡À}x~uDzUc|/¡Àr16|D|/qsTtD|wDD)cz æ c/·¨c&D|/c}Ucm»c|wtDDr)«$w}xuDz «$|rÆ|}Iw¤£Ø+{'r&}UD~u©wD|/¦{'r©6{'~uD}UcrDDrÌ8w v zUDrDyr Rc|Br$Dz6)|c}U8wÁv zxDr)ycr¬)|s&v y/|~uD«c|/wRu`{'¡Bcr)¨c¦c|r)cî}Uw{'zx«cr}x|~u©wx¡`{'zxrtD|/z{'ïº D}Iwza¨RczUDcr£B³Ø{w}¤{' ~uD|/~u+«vrD}UwxzxD|/czUcrÂÞF|/r)rDu$rD|~u©wY¢){'«©wÞNv }xDr)ycrÂ)cz |/rD¤{zx|}U|zUwr/c|/~u8)rDycrD}xvr)DczUrÂð { uDczUDrDy}U²v }UDrDyr+T|/wDzY}Uvyr`{'rDr©wr æ ËÄñ ¢wuDv8D'£ °1|rD}·Dcz°1zxy¡DrD|}U}xvr¯Þ\|/rDrDk8u8Ì|}Iw¤1`{'¿r$DzTr`{'~uD{') rDD+tD|zx{'Tv8Dcr¹|/rº }Uw{'¡D|/èN{'}Uv&{'r©6{'~uD}UcrDÍDrD(D{'|w¦}U|~u©w¡D{'z¦}U|rD£R®YD zD|qs}Iwzxv'rDvT||}UwD|/c}¦|r Z|~u©wx|y}Îa}xDw{wcÀRc|/çc}u\{ )`y!rD|~u©w+v y/|~u|}Uwc{')}Ä6wxz{'~u©w)rDycrƨc¿r$wx}x~uD|º Drv¡kt)|z{{'zU¬'vz{')}xc|/rD¯v8Dcz·r`{~uD{' crD(}U|rD£RªK|/~u©Z|zx|y'«'c|wZ|/zxÌ|r Ä6|/ã{'rDyDcwwcëªKDzx~u̪KvtDt)czU}x}UDrDyrÌ«{'rDr{'r¹¡À}Uwx|Trçv¡D|/8wzxrD {')DczRc|/rDyc¨c|/~uDrDwxcrÞF|/rD|Z}x|/~u¬{'DrÄ6cv'¡`{'~u©wz6¨c¦¡À¢6ycr¬v8DzN'vr¬|u)j6yD£ °1}´|/}Uw{'¡Bcz}x~u©Z|zx|y+¨cr©w}x~u)c|)crçv'¡DzT|/w·ÉvDzT|/w´ã¡À¨c|~uDrD¢w¬³Hc|/Dc} Îa{'rDD} DcòÄ6cv'¡`{'~u©wzr\{' uDz |}Iw DrD`{|w¤\v¡&D|/!tD|/z{'{'zxT·r`{'~uD{') rD¹v)cz v'z{'D}Uc|/cr)}x|r)£µ²}IwD|´Ä6Rcy)rDy}xzU|~u©w)rDyZ|/{'rDyyc¡Bcr)rD±ã¦DczKrF{' uDczU³Ø|Ñ `{'r)rÂ}x|/rDÂD|/´c|/rDy¨cc|/~uDrD¢wcrÆ8tD|zx{'{'zUr`{~uD{' crD£Bµ²}Uw É DczYr\{' uDzx/|cy'crDD³Ø|Ñ ó `{'r)r }x|/rD´D|/¶8tD|zx{'{'zUç'vz{D}x|rD£ªK|³uDvzx|/Rv'rÞF|r´)rD·u$´D zUD6¡Bc)c)wxcr `{'·³Hc|/\ã·r {' uDczU|/cyrD!¨cD½ÄRcv¡`{~u$wxcza}x|r DD£ 2 Bewegung Bewegung zum weg vom Beobachter Beobachter 1 ÖØ×ÕÙ Úô õ :<;>=:;>ö´=\M`=ØJ6CD; d G>eRGI=H;>@ÀAZVJKe¼W=\MXCDLR÷RE=ØGIG>=ØJK_aVKMDPR=Np æ c rDr·D|/6¡Bc}x~u)zx|¡ÀrDZ³uDcv'zx|6¨c)wxzx|/ÃBw¤ D}U|~u·{'rDzçvzx)czU zUvr©w1c|/rDc}1tD|zx{'{zxT} c|/rD·8wxv'Rc/´¡BDrDDcr£Fµ²~uÆ+v ~u©wu)|czsczx«$Ü{' zxrÀZ|/ ¦{rD|}x·8wxv'Rc/{')}KDcr t`{'zIw|/c/crªK|Ãzxcr©wx|{'/y|~u$DrDyr&ìD zTD|8wxzÁv )rDy±|rD}|/}xr$wxzxvtBcrÌ«'vTtDzUc}x}U|¡D/cr {'}x}oDr©wz1¡D}Iw{'r)¨c|u$DrDyK¡BczUc~uDrDr«{'rDr Dr) r`{'~uDt)z') r'v¡D|68wxv'Rc/crD«$DzI D|/K®`vzx^c|/rDcz¶tD|/z{'/K{'rDr)|T´w¤£$µ²ø¥Yr©wzx}x~u)|c¨c!ÞF|/r¬DrDu$!|/rD¤{'zU|}U|czUZ|~u!{'/}xv D|/a/c|~u$Dr)ycrTrD|~u©wc£©µ² r\{' ~uD}Iwr¬qs¡D}U~uDrD|wxwNZ||~uTD|Z°1zUyc¡Dr)|}x}UY)|}x«$)wx|zxcrTDrD T|/wDr+°1zUyc¡Dr)|}x}UcrvrÞF|r!DrD+u$'czUy|~uDr£ ªK|t`{'zIw|/c/crªK|/ÃÀczUcr©w|{'y/c|/~u8)rDycr! D zK)|$wz v' DrDyc|r)c}{'}x}KDr©wz°1|yrDyzx{º 8|/w{w|/vr}x|/rD ùú`û D|¿Ð ù©ü Ôêý Ò Ð ù©ü Ô úDûÊþ DD|/|/ÐÐ ù©ù©ü©üüÿIü ÔÔ Ð>ÉÏÔ û ý ù ý ù ªK|}x|~u$DrDy'cr}xv'r¬¨c´§UDcÊ»c|/wxtDDrD«©w NDr){r§UcD KzUw ý Ð ÿ ÔR|r)cz {'/}KDrDrDD|/~u± D rDr±{'rDy}xcu)crDr¹~uD|¡B·ycwcr£FÈY|/czx¡Bc|o|}Uw ù Ð UÔKD| ®o {' ~u)crDD|/~uº w ü Ð UÔ¶ý^Ð ü©ÿ ü ÔaD|/ 8wxz v ´DrDy}Uyc}U~u$Z|/rDD|/y«'|/wK)rD Ð UÔZDzªKzx)~«B£ÀªK|DzU|/wxwx c|/~u$DrDys|/}Uw`§UcDv8~u·{'/}Ø|rDR| y}{'´wxcrDzUc|/D|TcrD}U|vrD{'rÎa{'DzU D //w6c|/~u$DrDy ìD z`{'} zx{Á8|w{wx|vrD}UtÀvwcr©wx|{' Ð UÔ¨c|/rDcz´{'))cz °1¡BcrD·ýÊÒ«vrD¨cr©wzU|czIwr ®o {' ~uDcr)D|~u©w ù {') ¨)4{'}U}xcr£ªK|c}}U|rD&8|/czTc|/~u$DrDyr& D zD| D r)s¥Yr$¡À«{'rDr©wr ù ü©ÿ ü {'}Uv¡)z{'D~u©w6¦{'rTc|/rD6|/wxczxK/c|/~u8)rDyD£$ªK|}|}UwRD|/a«vrD}Iw|/wx)w|s/c|ïº ~u$DrDyDHD|/|rDr»D}{TcrDuD{'rDy¨Z|}U~uDcrªKzUD~«¿DrDªK|~u©wuDczU}Uww¤FDrDD|T¡À| |}Ucr©wzUvtBczY8wz¤v Dr)yT)|®`vzx ý ! $ù # " u`{w6|w¶Ëvr)}Uw{r$wxc%r !'&(Ò )( &É µ²~urDcu){r|/r¬Dz~uD|¡BK}x||r¬¨c|/wx|/~u¦}Uw{º w|/vr\{' zZzUv'w|/czxrDD}tD|/z{'/ D}UwxczZvzUu`{'rD)cr£Àµ²~u}xD~uD·{}xv¦ÞNv }xDr)ycrÀDczUcr¨c|/wx|/~uD qs r)DczUDrDyr8)z|/rÆ|rDzÎavw{wx|vrT|/w æ |/rD«'y}x~u©Z|r)D|y«c|+w *D¸Dr&|/wxwxc/tDDrD«©w Dz~uD|¡B ¡Bc}Uwxcu©w¤ÀDczs|¼¥YzU}xtDzUDrDyD}Ëvv'zxD|/r`{wrD}U8}IwcT}s/|ycr}xv/è£`µ²ríHv{'z>º «'v8vzUD|r`{wc)r , - DT{'/}xv·y/wr ù Ð , .-/ UÔêý ù 0Ð , - 1*2 ÒÔ 0Ð , -3 UÔ ý 0Ð , - 1*2 Ò©Ô ü 0Ð , -3 UÔ ý 4´Ð *2UÔ ü Ð , - 1*2 Ò©Ô Rv¡À| 4´Ð *2UÔ´c|/rD6ã 5ãÆ+{wzU|&|}UwcçD|/!«©wvzUcr¯|/8 7 )éDcr æ |r)«'c *2Dzxu©w¤£ ¢w¨w+¦{r<D|}x±qsD}UDzD ~«|rD{'}|~u$DrDy}U}U8}Uwxc ÐIÉÏÔc|/rYD{'rDr'czx}U~u©Z|rDDr D|/¯»|/w{'¡D|/wxDrDyrKDrDj¦{'rczUu\{' w±|rj/c|/~u8)rDy}x}I8}Uw ) z±D|/¥Yr$¡À«{'rDr©wr ù Ð ÀÔý ù Ð ÒÔ ü Ð ÀÔý ü Ð Ò©Ô Ð ÀÔ¦ý Ð Ò©ÔçD{'}·|rDcrDzU}xtoD r)y|/~uDcr«{'zUwxc}x|ïº }x~u)crÂËv8vzx)|r`{wxcrD|/®Ov'zx 9*sÐ ;:%< Ô ùKû D|¿Ð ù©ü Ôêý Ò D|/Ð ù©ü©ÿIü Ô û * ù©ü : 9*sÐ ;:%< ÔcÐ ù©ü Ô û þ ÐÑãÔ û ý ù D|/Ð ù©üü Ô ý = ù ý ! $ù #> u`{wc)Rv¡À| !ýjÐ ÿ Ô : ý ?Ð @ ÿ Ô ü : ýjAÐ ü ü©ÿ Ô6}xc|/cr£ qs/zxD|/rDy}|/}UwHD|}x}ç|~u$DrDy}U}U8}Uwxcr$Dz\|rDr§UcrD|/ycr´í1DrD«©wr czIìD w¤c)|rD|~u©wØ{') 8wxv'Rc/crD«$DzIr´|/cyrcRc|/ ù DrD ü r$wx{'r)ya'vr $wv'Rc/r|rDr t)zxDrDyau`{'¡BcrDrD }xv'|wrD|~u©wRD|/ÃÀczUcrD¨|czU¡`{'z}x|/rD£©qYD}R)cr!c}Uw¨cr¬)cz6+{'}x}UcrºoDrDµ²t)D}UczxuD{'/wxDrDy «{'rDr&{'r§UcDv8~utDzUDrDy¡Bc)|rDy)rDycr±ìD z ù Dr) ü uDczUc|wr\D|T|r§UcDòí1DrD«©Bw Dz8wv''6/crD«$DzIczIìD ws}Uc|/rÆD }U}xr£®Y) zK`{'}Ku)|czYDr©wzx}x)~u$wx¦í1zUv¡D¼rDcuDTcr C D|/c}xÄ6D|r)yDrDyr`D|/¦{'r{')~u+Îa{'rD«$|r)¢º>ÈaDyvr)|v'wZÄRcD|/rDyDrDy'crrDcrDr©wcB)|®`vzx *sá ù Eå D%<E;: ý á ù DF< ü å *sá ù©ü Eå D%<E : ý á ù©ü D%< ü å û D1á å {'r£OÈa|zx¡Bc|F|}I=w DÂG ý DçÐ ÀÔc|r°1|rDu)c|/wx}U'c«©wvzODcza|½í1Dr)«$=w }UcrD«$zx~u©w{')oDczs8wv'º Rc/}Uwxcu©w¤ODrD Iá H Ð ÀÔ²åBJ ý HLKoÐ ÀMÔ NHOØÐ ÀÔ DztDzUDrDy¹Dz®`DrD«©w|/v r H | í1DrD«©Pw ÍDz8wxv'Rc/'3£ H K |}UwDz æ zUw¬{')DzIº §Ucr)|yr8c|/wxDcz8wxv'Rc/'{')RD|Q DçÐ ÀÔK¨c|y'wcR H O )cz æ zUw{'6Dz{'rDDzxcr|/w£ ËcrDr©w1{'rD| æ zUw ù O Ð ÀÔ xü O Ð ÀÔØ)rDDcrT8tDzxDr)y·á ù Ð ÀÔ>å©`{'rDr«{'r)r ¦{r{'D}ØD|}xcr c|/~u$DrDyr¦DrðYvzU¦{cr©'c«©wv3z D1Ð ÀÔR{')}xzx~uDrDr£ æ c|/; DçÐ ÀÔD|YÎa|/~u©wDrDyDcz¶8wv'º Rc/s¡Bc}Iw|T´wc8«{'r)r¦{'r¦uD|z{'D}6c|r)KªK|/ÃÀczUcr©w|{'y'c|/~u$DrDyìD z¶D|/8wxv'Rc/crD«$DzI uDzx|/wxcr`{D}ZDczZ{'r!D|}xËDzU'¡BczUc~uDr)cr«{'rDr£ S =\f$CHd b CD;IeN=HJ W;I=]+M`eN=VUJ;Iff)=W;I=:<;>@BA6CD=FE&=HGIGI=HJ6CDAK=HLNMO;>=XW T qs)}D|/c}UczªK|/ÃÀczUcr©w|{'y/c|/~u8)rDy¡Àzx~uDrDwx8wxv'Rc/cr)«8)zUr± D z¨¢6|N'czx}U~uD|Dcr) æ czUwx+Dz æ |r)«'c/yc}U~u©Z|rDD|/y«'|/w *î}x|/rD(|rÌDcrgÄR|)czxr ó Dr) `{'zUyc}Iw//w¤£NÈa|cz>º ¡Bc|KZDzUD±¨|rDz!'vzxy'cy¡ÀrDcr<zUv'w{w|v'rD}x}ITTwzU|}U~uDcr¶{'}UvÌr$Dzv' qs¡D}Iw{'rD v' »cr©wxzxD Dcz{'{Ï)|/ {'¡)u\{' rDy|/ycr¿ªK|/~u©w'czIwc|/Dr)y ù `{}zx{¤|w{wx|vr)}xtBv'wr$wx|{' Dr)´`{'r)rD|/NÎav'w{w|/vrD}Uyc}U~u$Z|/rDD|/y«'|/w ü ¡BczUc~uDrD¢w¤£ª{'}Ø{}H)«$zx|}IwØD{'}Ø»cr©wzUD Dz{'{|/Z{')F«vrD¨cr©wzx|/}x~uDrËzUc|/}xcr£)ªK|/YÎZv'w{w|/vrD}xy'c}x~u©Z|/rDD|y'«'c|w6uF{' rDy'wNvr)cz ªK|~u©wxzUwxc|/DrDy+{'¡Dr)&|}Iw)Dzx~u¹D|/¦ÞN{' r)y)cz íç |·`{zxy}Uww¤£H+{'rczxuF{' /w{') D|/c}x æ |}xc|/rD¬¢){'«©wx!ÞRv' }xDrDy+Dc}T|~u$DrDy}U}U8}UwxcT}!Ðèã'Ô¢£çªK|/c}U¦zxvw{wx|vrD}U}U8Tìº wzU|}U~uD ÞNv }UDrDy¦r©wu\{' ws«c|/rD8wxv'Rc/crB)rD+DzKÎZv'w{w|v'rD}xt`{z{'Twxcz *k}UtD|/wa«'|rD ÎZv/'£ µ²~u¿rDcu)r$DrÆ{'r`{'¨c¿|rD?yyc¡BcrD æ czUwsvYr *`{'}|~u$DrDy}U}U8}Uwxc ÐÑãÔ c|/rDÞ v }UDrDyu`{wc)D|/K}x~u©6{'~uD´8wv''6/crcr©wxu {' /w¶DrDD|/K}x|/~ur$DzR6rD|yv'rDczzUvº w{w|v'rD}x}ITTwzU|}U~uDcr·Þ v }UDrDyDr©wzx}U~uDc|/Dwc£$ªKDzx~u·Dr¦zxrD¨ ) ¡Àzxy©{'r)yTá ù [å Z Ò{'/}xv ù K ù O Z ù ü K ü O Z ü 'czUc|r4{'~u©wK}x|/~uD{'rDrD|ªK|/ÃÀczUcr©w|{'y'c|/~u$DrDy´ D z)|8wv'º Rc/crD«$DzI£ÄRcz) ~«8}U|~u©w|/y'wH¦{rr)v~uÁD{'ZD|Nc}U~u$Z|/rDD|/y«'|/w ü ¡Bc|©DzFvzU|ycr)Dcr \ ÞNv }x)rDyTw{'rDyr©w|{F{'r!«'vr)¨ccr©wxzx|}U~uD ËzUc|}U|}UwcDczUu\{' wZ¦{'r!D|/ªK|/ÃÀczUcr©w|{'y/c|/~u8)rDy ,DÐ - Ô ] ,)Ð - Ô1ý Ðó Ô ^ ] ; O h i h Ð _a`cbedgf Ô kÉ j ìD zD|/síHv{'zU«'v8vzx)|r`{wxcr0Ð ,)Ð - Ô - ÔçDz¶$wv'Rc/rD«$DzU''$6v¡Bc[| kÐ ÀÔm ý l ] Ð ù aÔ n ] ù )| ~u`{y'c}x~u©Z|/rDD|y'«'c|wT¡ÀDc)wxwc£RqY}TÞNv }xDr)y±D|/c}Ucz¦/c|~u$Dr)y±zxu\{' wT¦{'rÌt)|z{cr v'rÌDrDcrÌ|rDr(Ä6|/Dzxr ó DrD §U¢6|}·¨¢6|a|rDy'c¨c|~uDr)w}x|r)£ªK|} ·D zxD{'ïº }xv!¡Bc}IwÏ{ wx|yrF`{'tD|/z{'{'zxT ªK|/~u©wRc/rÆ}U|rDD|·{rÆ)czvzx)czU zUvr©wDDzx~uÆc|/rD 8wxv'Rc/¡Bcy'zxcr)¨w}U|rD£ æ c|68wxv'Rc/cr±D|}x!t)zx|{/ vzU¸u`{'¡BcrØÆ) }x}xr{'D~u&)| uD|/r$wxczDr8wxv'Rc/cr!uDzx{') cr)DcrªK|~u©w¢6/crtD|/z{' vzx^u`{'¡Bcr£ ªK|Y|rDr+ÄR|)czxr¦yc¨c|ywcr8wxv'Rc/cr!rDDcr!|/ǵ²rDrDzxr{'r!c|/rDcÇËzxc|/}c8ìD zDc}U}xr Îa{'D|)9} , y|w ,Hoqp ü pJ ý k µ²Åµ²rDrDczUcr¿D|/c}x}Ëzx|}x}K|}IwKD|/´|/rÐ ó Ôa{')àwxzxwxcrD) æ DzU¨cçrDcy{w|ÀBDrD¡Bc}U|/wx¨wK)| ªK|/ÃÀczUcr©w|{'y'c|/~u$DrDy´D{'uDczZ«c|r)¦Ð zxc/ÁÔ6ÞNv }UDrDyD£B$wv'Rc/r«Àv r)rDcr{'}Uv·r8)zY{Dcz>º u`{'/¡!D|}xc}aËzx|}Uc}Z¢|}Iw|/czxr£ ªK|}uD{w v'yrDDcr&zUDrDëت{'}´/c|/~u8)rDy}x}I8}Uw ÐÑãÔ|/}Uw6Dcz´u$8tBczU¡Àv/|}U~uØr)v~u c/|/t)w|/}x~uDr)v~ut`{'z{¡Àv/|}U~u£O®sD za`{'}aqs)àwxzx¢wcrvrÂ8wv6r}UtD|/wY{'¡BczaD|DzU|/wxwx c|/~u$DrDyvr(ÐèãÔ·Ð D|TíØvwcr©wx|{'/y|~u$DrDy$Ôs«c|/rD¦ÎZv/'À}xvr)DczUrr$DzD|·czU}Uwxcr¡Bc|ïº Dr£Øwx¨w¦{'r {}¡À«{'rDr©wvzx{'D}cH`{'r)r±}U|rDÆD|·zx}Uwxcr±¡À|Dr&|~u$DrDyr±|r c|/~u$DrDy}U}U8}Uwxcø) z6D|/K¥Yr$¡Bc«{'rDr©wxcr ù DrD ü D}x}Ucr!³N8t!¡Bc}Uwx|T´wN6zxDr«{'r)r£ +{'r!`rD)w¤`D{'·D|}xc}sc|/~u$DrDy}U}U8}Uwxc½u©8tÀzx¡Bv|/}x~u|}Uwc)4{'/} ü pr&sk |}Iw¤ç6{'}¦|/ézxvw{wx|vrD}U}U8T¢wzx|/}x~uDr¯®O{'/¶|rDz¦ÎZcy|/vr{'Dzxu`{¡Dc}¦ËzUc|/}xc}Ty|//w¤£ µ²rDrDzxu`{¡·Dc}NËzx|}Uc}1|}Iw`{'}N|~u$DrDy}U}U8}Uwxcß`{ycyr/|t)wx|}x~uDr)· v'y/|~u rDDcr D|/Â8wxv'Rc/cr¯{' Ëzxc|/}c1Z|sÞ v }UDrDyr(c/|/t)w|/}x~uDz¬|~u$DrDyr¯«c|r)¿8wv''6/cr cr©wxu`{'/wxcr« v rDrDr£ p H=;:% t hyperbolisch elliptisch 10 20 R ( = Abstand vom Zentrum) Bild 3: Rotationsgeschwindigkeit des Spiralmusters: Omega = 0.18 hyperbolisch elliptisch 10 20 R ( = Abstand vom Zentrum) Bild 4: Rotationsgeschwindigkeit des Spiralmusters: Omega = 0.4 u æ c |O{)Dr¬Ä6|/Dzxr·vr¬{{|rD|Yt)|z{{'zUD)zx~u¦)|Zy©{'rD¨K8~uDc|/¡ÀrDzxy|vr¨c {) cr}x~uD|rDrB¡ÀDc)wxwYD|}cO`{'TDzY|/t)w|/}x~uDÄRczx|~u|rDrDzxu`{¡Dcza«$Dyc v zxT|º yrk»cr©wxz{'/zxcy'|vrDcz¦{'{|//|ycr DD£çs||~u©wT}Uwx|T´w·D|+~uD|¡B+T|/w·D u©8tÀzx¡Bv|/}x~uDr¯Ä6zx|~u D ¡Àzx|r1D|/«$Dyc v zxT|y'¬ÎZcy|/vr¹|wDéc/|tw|}U~uDcrÄR¢º zx|~u£ +{'r}x|/cu©wo{'r)crÄ6|/DczUr ó DrD ÁDrD{'r«{'r)r}o{')~u}Uv' vzUwØ{'rDzoªK|Ãzxcr©wx|{'/y|º ~u$DrDy+Ð ó Ô¶{¡D}xcr``{'v'ÃÀcrDt)|z{{'zUY¡À|«$c|/rDczZÎZv'w{w|/vrD}xy'c}x~u©Z|/rDD|y'«'c|w *ÌDc} tD|/z{'/ D}IwczU}·{')àwxzxwxcr1rDyÆyZDr)DcrDÂtD|/z{'{'zxT¦¡Bc|yzUvz·Îav'w{w|/vrD}Uyc}U~u$Z|/rº D|/y«'|/w¤£Bqs)}DczªK|/~u$wxRc/cr©wxuDcvzU| ´D¦{r¿{'}Uv¬}x~uD/|cr`{'¬ìD z{'{|crB)| |r¦DczZÈaD¡D¡D/¢º>Ë{'}x}U|/`«{wx|vr¨cDø³N8t+){ ycuFv zxrDD|/tD|/z{'{'zxTYu)vuDÎZv'w{wx|vr)}xyìº }x~u©Z|/rDD|y'«'c|w¡À}x|/wx¨crFìD z~¢º>{'{|r`{'yycr±rD|Dzx|/yÎZv'w{wx|vr)}xy}x~u©Z|rD)|y«c|/wc£ qs)~u¬D|Zv'r¬ÞF|rTDrD!8u8¦|rT|uDzUcz³uDcv'zx|YczUu`{'/wxcrDrt)|z{/Rc/cr v/ycrT|jRc}Ucr©wUº |/~uDcr)crTuD|zç¡Àzx~uDrDwxcr¬8wv6r£qY}xvzxy|/¡)w1}U|~uT{'D~u{'D}1|/uDzxz1³uDcvzU|D|/c}Ucz DrDD{'r©w{'/ »D}x{'TrDu`{'rDy¨Z|/}x~uDr±ÎZv'w{w|/vrD}xy'c}x~u©Z|/rDD|y'«'c|wKD}tD|/z{'/ D}IwczU} DrDv sÃrDuD|/wZDrD°1rDyDczYt)zx|{{'zU£ Ó'c)v~uÂ}U|rDD|ÎZc}UD/w{wrD|~u©wsy©{'rD¨}xvc|r)Dc)wx|y·Z|¦{r}U|~u+D r)}x~u©w£ªKcr)r¡À| «$|rDzçÎZv'w{wx|vr)}xy}x~u©Z|rD)|y«c|/woZ|zx´D|¶/|t)wx|}x~u)6ÎZcy|/vrD|6|Ëczxr·Dz{'{|/ cr©wxu`{'/wxcr}Uc|r´DD8yzxv)D{'/}xv ) Dcz¶Ëzxr!yzUv´Rczx)cr){ uDzxrD!D|ÄRcv¡`{~u$wxDrº yrD zØ~ìºI{'{Ï)|/cryz{'DNc|/rDcr«$|rDr´ËczUrzxy¡Àr£³ØzUv'w¨Dc ¡BcD)w¢wo)|c}HrD|/~u$wc `{')|ªK|/~u$wxRc/cr©wxuDcvzU|64{}x~u}Uc|/rT´DDRc|/)D|/¶qs)}xDuDr$DrDy´)czç|/t)w|/}x~uDrÎZ¢º y|/vr+{D~u'vr{'rD)czxr¿zÁv rZ|/)czYÎav'w{w|/vrD}Uyc}U~u$Z|/rDD|/y«'|/wYDc}K{'}Uc}aDrDÂ)cz v'«{cr~uD{'/yc}U~u$Z|/rDD|/y«'|/wR{'¡Du\{ rDy'w¤£$°1|/rDYrDDy) /w|/yZ°1r©w}x~u)c|)DrDy+D ¡BczND|Z³uDvº zx|/Z|/zxÂRvuDçzx}UwKÂv y'|~u}x|rB6rDr±{'rÂ|rD´¦{wxuDc{wx|}x~u)´³uDvzx|/ ¨cDzÞNv }UDrDy D}yc}x{'´wrÆ/c|/~u8)rDy}x}I8}Uw}ÐÑãÔa|/ DzUc|/D|TcrD}U|vrD{'r+Îa{'DÅ¡À}x|w¨wc£ªK|/c}K/|cyw uD)w¨)w{'y'{¡ÀzY{DczUu`{'/¡)czaÎa|~u©Rc|/wxDczZ{wuD¦{w|}U~uDcr!qYr`{'/8}U|}c£ w =yxì=HM`=HJK@F=\f áâÉcåÓ)£OÄ6|/rDrD'OÀ£`³Hzx¦{'|/rD'ë`{'{'~wx|~Y)8r`{'T|~c}£`í1zx|/rD~c¢wvr¥Yr)|/zx}U|/w²!í1zx}x}Àí1zU|rD~¢º wv'r±Éz u t z á ãåÝs£ÕÝs£ÞF|r|{ £I{ £Þ\{'ëBªKrD}x|w²6{¤ wxuDcvzIv'1}xt)|z{H}IwzUD~wxDzx}v'1y©{'{|}c£B8wxD£ qst)tDè£B+{wu£ }~ÆÐIÉ z t z©Ô¢ z t ñBÉ \ó ÉÁÒ
© Copyright 2024 ExpyDoc