03 Dynamics Lecture Slides 2 of 4 2011

7/31/2019 03 Dynamics Lecture Slides 2 of 4 2011

1/39

Grkiobl|Falwq}a *=/7"


2/39

Kasw`k| 9|w Fis `h O`wb`k *Fis `h Bka}wbi"

Bk wja im|akla `h azwa}kif h`}la|&

ik `mnalw iw }a|w l`kwbkqa| w` ma iw }a|w ikgik `mnalw bk o`wb`k l`kwbkqa| w` ma bk o`wb`k

sbwj l`k|wikw xaf`lbwr *qkbh`}o |uaag bk i |w}ibcjw fbka"

@}bcbkif |wiwaoakw `h Kasw`k| 9|w Fis

Bk wja im|akla }a|qfwikw h`}la|&ik `mnalw iw }a|w l`kwbkqa| w` ma iw }a|w ikg

ik `mnalw bk o`wb`k l`kwbkqa| w` ma bk o`wb`ksbwj l`k|wikw xaf`lbwr *qkbh`}o |uaag bk i |w}ibcjw fbka"

O`gbhbag xa}|b`k `h Kasw`k| 9|w Fis q|a wjb| xa}|b`k+


3/39

Qugiwa r`q} falwq}a k`wa|


4/39

Kasw`k| =kg Fis `h O`wb`k

Wja }iwa `h ljikca `hoòakwqo `h i m`grb| u}ù`}wb`kif w` wja kaw h`}la wjiw ilw| `k bw&

ikg wja oòakwqo ljikca wida| ufila bk wja gb}alwb`k `h wja h`}la+

oxgguH

"*??

gwgw

gw

ogx

gw

xgo

"*"*$?

oiH?

L`k|wikw oi|| L`kwbkq`q| oi|| hf`s u}`mfao+gw

ogxH

"*?


5/39

Kasw`k|


6/39

Kasw`k| =kg Fis `h O`wb`k *Xbga`"

jwwu>//sss+r`qwqma+l`o/siwlj0x?Z1w`DHF@~b5(K]?9


7/39

J`s w` |`fxa H?oi u}`mfao|0

Sjiw b| wja akcbkag}bxbkc h`}la0

Sjiw b| wja

illafa}iwb`k `h wja

ws` xajblfa|0

Sjiw b| wja wak|b`k

bk wja w`s/mi}0Sjiw b| h}blwb`kif

h`}la `k wja w}qld

mabkc w`sag0


8/39

J`s w` |`fxa u}`mfao| bkx`fxbkc H?oi

\wau *9" > G}is iff m`gba| \wau *7" > ]a|`fxa h`}la| h`} ailj izb|

\wau *=" > G}is HMG h`} `mnalw \wau *


9/39

YQB^ / ]aliuBk i h}aa/m`gr gbic}io h`} i |bkcfa`mnalw& g` r`q g}is>

I+`kfr wja h`}la| ilwbkc `k wja `mnalw

M+ `kfr wja h`}la| wja `mnalw aza}w| `k`wja} `mnalw|

L+ m`wj wja h`}la| ilwbkc `k wja `mnalwikg wja h`}la| wja `mnalw aza}w| `k`wja} `mnalw|


10/39

Azioufa 1> L`kkalwag m`gba| u}`mfao

Ws` oi||a| `h = dc ikg < dc i}a }a|wbkc `k i |o``wj wimfa ikg l`kkalwag

mr i wiqw |w}bkc+ I h`}la `h =5 K b| iuufbag w` wja < dc oi||+ Liflqfiwa

i" wja illafa}iwb`k& i& `h wja |r|wao&m" wja wak|b`k& W& bk wja |w}bkc+

i ? 0

W ? 0


11/39

HMG h`} = dc oi||

HMG h`} < dc oi||

L`k|bga} HMG `h l`ombkag oi||a|


12/39

HMG h`} = dc oi||

mild


13/39

HMG h`} < dc oi||

mild


14/39

L`k|bga} HMG `h l`ombkag oi||a|

\`fxbkc wja < ayqiwb`k| cbxa> i ? 7 o |/= 4 W ? : K

mild


15/39

Azioufa 8> Fbhw U}`mfaoI oi|| `h = dc b| jqkc h}`o i |u}bkc mifikla bk ifbhw+ Sjiw g`a| wja |u}bkc mifikla }aig sjak wjafbhw b|

i" |wiwb`ki}r+m" i|lakgbkc sbwj ik illafa}iwb`k `h 5+= o |/=

l" i|lakgbkc sbwj i qkbh`}o xaf`lbwr `h 5+91 o |/9

g" i|lakgbkc sbwj i galafa}iwb`k `h 5+= o |/=

a ga|lakgbk sbwj ik illafa}iwb`k `h 5+9 o |/=

h" bh wja fbhw limfa m}`da+*I||qoa c ? 95 o |/= "

Hbc+ *i"> HMG `h wja = dc oi||Hbc+ *m" W ? \lifa }aigbkc k |u}bkcmifikla+

\bobfi} u}`mfao


16/39

W W

W

oc

W

oc

W

oc

W

oc


17/39

L`k|bga} HMG `h = dc oi||

*i" Fbhw b| |wiwb`ki}r *m" Fbhw b| i|lakgbkc i?5+= o |= *l" Fbhw b| i|lakgbkc i?5l`k|wikw xaf`lbwr

W ?0 W ? 0 W ? 0

Wida qusi}g| i| u`|bwbxa gb}alwb`k

i?5+= o |=

i ? 5 i ? 5

oc ? =5 K oc ? =5 K oc ? =5 K


18/39

L`k|bga} HMG `h = dc oi||

*g" Fbhw b| i|lakgbkc sbwjgalafa}iwb`k `h 5+= o |=

*a" Fbhw b| ga|lakgbkc sbwjillafa}iwb`k `h 5+9 o |=

*h" Fbhw limfa m}aid|

W ?0

W ? 0

W ? 0

Wida qusi}g| i| u`|bwbxa gb}alwb`k

= = =

oc ? =5 K oc ? =5 Koc ? =5 K

++

H}aa hiff

\u}bkc k`w azwakgagW ? 5 K

Sabcjwfa||


19/39

ufq| |bck


20/39

Sabcjw x|+ Oi||Oi|| b| i oai|q}a `h bw| bka}wbi+Bw b| i |lifi}+

Bw b| ik bkja}akw u}`ua}wr& bkgauakgakw `h f`liwb`k`} |q}}`qkgbkc|+

Sabcjw b| wja oai|q}a `h c}ixbwiwb`kifh`}la `k wja m`gr mr wja ai}wj+Bw b| i xalw`}+Bw xi}ba| h}`o ufila w` ufila+


21/39

YQB^Sjblj h`}la b| wja sabcjbkc oiljbka oai|q}bkc0I+H}blwb`kif h`}la

M+Sabcjw `h oikL+L`kwilw h`}la `k sabcjbkc oiljbka mr oik


22/39

SabcjwSabcjw `h oik b| wja

c}ixbwiwb`kif h`}la ilwbkc mawsaak wja ai}wj ikg oik&

k`w mawsaak wja sabcjbkc oiljbka ikg oik+


23/39

Sabcjw x|+ Iuui}akw Sabcjw Sabcjw `h ik `mnalw `k ai}wj }aha}| w` wja c}ixbwiwb`kif h`}la `k

wja `mnalw mr wja ai}wj+ *S ? oc"

Iuui}akw sabcjw `h ik `mnalw }aha}| w` k`}oif l`kwilw h`}laazua}baklag mr wja `mnalw+Bw lik ma oai|q}ag mr wja sabcjbkc |lifa `} wja |u}bkc mifikla+


24/39

KK

K

K?5

SSabcjw `h wja oik+ L`k|wikw bk iff li|a|+ K`}oif l`kwilw h`}la `k oik *K" gbhha}|+

K Iuui}akw sabcjw `h wja oik+

Sabcjbkc oiljbka lik oai|q}a iuui}akw sabcjw& |bkla K? K mr K


25/39

R`q azua}bakla sabcjwfa||ka|| sjak wja}a

i}a ++ `k r`q+


26/39

Bk|wikwika`q| x|+ Ixa}ica H`}la Bk|wikwika`q| H`}la

gwguH?

Ixa}ica H`}la

w

uu

w

u

H

bh

?

?;6


27/39


28/39

Sjblj jbw ji| i mbcca} bouqf|a0


29/39

Bouqf|a ikg Ljikca bk Oòakwqo H}ò Kasw`k| =kg Fis

Bkwac}iwbkc&

gw

guH?

uw h

=

bh

uw b

9

Bouqf|a

Bouqf|a Ljikca bk oòakwqo


30/39

Bouqf|a ikg Ljikca bk Oòakwqo Bouqf|a b| i xalw`} *|bkla oòakwqo b| i xalw`}"

\+B+ qkbw ? K |

Mi|a \+B+ qkbw ? dc o |9

\ioa i| qkbwh`} oòakwqo


31/39

H`}la/wboa c}iuj *H/w c}iuj"Bouqf|a ? H gw ? i}ai qkga} Hw c}iuj

? ljikca bk o`oakwqo `h wja `mnalw

L`k|wikw H`}la

u ? i}ai qkga} c}iuj ? H

w

Xi}rbkc H`}la

u ? i}ai qkga} c}iuj ? gwH

w

w

=

9


32/39

O`oakwqo/wboa c}iuj *u/w c}iuj"

gw

guH?

gw

gu? c}igbakw `h uw c}iuj

? bk|wikwika`q| kaw h`}la `k wja m`gr

w


33/39

O`oakwqo/wboa c}iuj *u/w c}iuj"

w

uH

;?6

w

u

? c}igbakw `h fbka |acoakw n`bkbkc w9 ikg w=+

? ixa}ica kaw h`}la `k wja m`gr

wwH

bh

?

?;6

uw


34/39

Bk \qooi}r

Hw c}iuj> I}ai qkga} wja c}iuj cbxa|

ljikca bk o`oakwqo *bouqf|a"ljikca bk o`oakwqo *bouqf|a"

uw c}iuj> C}igbakw cbxa| wja ++ilwbkc `k wja m`grkaw h`}lakaw h`}la


35/39

L`klauw `h ixa}ica h`}la

Ixa}ica H`}la 6H;

6H; b| lj`|ak |qlj wjiw>i}ai qkga} l`k|wikw 6H;w c}iuj ? i}ai qkga} xi}rbkc Hw c}iuj |`wjiw m`wj cbxa wja |ioa bouqf|a

]aif h`}la b| q|qiffr k`w l`k|wikw+

Sa lik iuu}`zboiwa sbwj 6H; ilwbkc `xa} w+


36/39

= o|/9

w ? 5 |

w ? 5 w` 8 |

w ? : |

u h? 0H

* " G w b *b" wj w h wj m g w wb w :


37/39

*i" Gawa}obka *b" wja oòakwqo `h wja m`gr iw wboa w ? : |*bb" wja ixa}ica h`}la `k wja oi|| *h}ò w?5 | w` w?: |"

*i" *b" Ljikca bk oòakwqo

u ? i}ai qkga} H w c}iuj

? *8 $ 7" z 95

? 15 K |uh? ub $ u

? oxb $ 15

6H;

*bb" 6H; w ? u

6H; z : ? 15

6H; ? 8+ < K

w ? 5 |

H

w ? : |

u h? 18 K |u b ? 8 K |

u ? 15 K |

*m" G w b wj w h wj m g w wb w : bh wj h w g


38/39

*m" Gawa}obka wja oòakwqo `h wja m`gr iw wboa w ? : | bh wja h`}la ilwagb+ ùu`|bwa w` wja gb}alwb`k `h xaf lbwr+

bb+ ua}uakgblqfi} w` wja gb}alwb`k `h xaf lbwr+*m" *b"Wida xalw`}| bk wja gb}alwb`k `h xaf`lbwr i| $xa+

Wjak& u ? / 15 K |

uh? ub $ u

uh? oxb $ */15"

*Oòakwqo ljikca ifsir|wida| ufila bk wja gb}alwb`k `hwja kaw h`}la)"

/ /

Kaciwbxa |bck m`gr k`s o`xa| ùu`|bwa w` bw| bkbwbif gb}alwb`k+

w ? 5 |H

w ? : |

77 K |15 K |

u b ? 8 K |

*m"*bb"


39/39

uh? ub $ u *XALW@] ayk)"

vubv ? oxb ? *

Mr Urwjic`}i| Wjo&

u ? 89+8 d o |/9

*m"*bb"

Gb}alwb`k>

? wik/9*158" ? :

03 Dynamics Lecture Slides 2 of 4 2011

Documents

Transcript of 03 Dynamics Lecture Slides 2 of 4 2011