Multiple scales

Using complexvariables

Utt U E Ut Uit UH 12N

Expand u Ult s s et

U U tell t

Nott t Uo 0

Us t U Uf 2Uots

Uo A Et t A eit

since u.ae EgAcomplex A Acs CCl

Aeit c.cacomplex conjugate

Uf A'edit YA A Ahe2 it

Uots i As e t c c

Htt u i'tfAF It tiffins

Eliminate resonance A O Acsi A

No Et scaleNeed aft scale to determine

amplitude frequency corrections

Let t e't it it

U Ult s t

d Utt U.tt 29 Uts 292Mt tda k

fuss 128 Use E U

U No EU Uz

Nott t Uo o

htt t U eu2

UG Uo A eit.ae IIA5 A Ae

Ui tf t U U 24

Atelite 2A a Ahe 2 it

Solie for Us u Aye'itIII atA e

Beit c c74

BE o

Okiu us 2U.lt 2 29

Why Bs o 7hI C 461 08 a Not E U t 0

U o o

UoE a at t o

U o at t o

U o at t BIfanof AB Bce

U2tttUz 2Uoy 2UoqiAeittc.Uo

A lit c c

U 2A A LzAethit Iz A2e2 it

LAA

UzttxUz eit 2ftzA'A 2 Ati

eits Ec t

Eliminate secular resonant terms

A A

qiA

un Aeit A eit

LethuA Reid Rupe R

U Reitt 9 Reitt 19

LR cos TtyAr Retiree ei9Retiree i 5123

R Cfe Iz Rs Re o

9e R

u srcosiiaz.iie.MIL