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VED1
E L-LOVELY-H math10-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N
fJ;h soQK HHHH(15)

(fJZE, & ehws gqGkt j? feT[Afe p 2 ns/ y d/ ;fEo ofjD s/ p 2 gfotosB j'D d/ ekoB q 1
ftZu gfotosB j'fJnk j?.)

;wheoD (11) ftZu d'B'A gk;/ dy dk Gkr d/D s/ p 1 ns/ p 2 ;fEo wzBD s/ (Gkt dp 1 = 0, dp 2 =
0).
fJ; soQK

HHHH(16)

fJZE/, nkwdB gqGkt B{z do;kT[Adk j? feT[Afe fJZE/ p 1 ns/ p 2 ;fEo ofjD s/ y ftZu
gfotosB j'D Bkb q 1 ftZu gfotosB j'fJnk j?.
id'A fe;h t;s{ dh ehws ftZu gfotosB j' iKdk j? sK T[gG'esk dh ;zs[PNh ;so ftZu th
gfotosB nk iKdk j?, fJ; bJh T[gG'esk ;zs[bB th d{i/ j'o T[dk;hBsk teo T[Zs/ ;Ekfgs j'
iKdk j?. wzB fbU ehws gfotosB dh jkBhg{osh nkwdB gfotosB Bkb eo bJh iKdh j?
ns/ T[gG'esk T[;h T[dk;hBsk teo T[Zs/ pfDnk ofjzdk j? Gkt T[;dh ;zs[PNh ftZu e'Jh
gfotosB BjhA j[zdk j?, Gkt dU = 0, fJ; soQK
U = f (q 1 , q 2 )
Gkt dU = f 1 dq 1 + f 2 dq 2 = 0

gozs{ ;kB{z gsk j? fe , fJ; bJh

p 1 dq 1 + p 2 dq 2 = 0
fJj wkB ;wheoD (9) d/ fsZi/ Gkr ftZu oZyD s/
dy + q 1 dp 1 + q 2 dp 2 = 0
fJ; soQK ;wheoD (11) d[nkok

U = ;fEo (Constant)

fJ; soQK ;wheoD (14) B{z d[pkok fbyD s/

U = ;fEo q 1 ehws & ;fEo HHHH(17)

ehws gqGkt gqfs;EkgB gqGkt nkwdB gqGkt
;wheoD (17) ;bN;eh ;wheoD ejkT[Adk j?.

Nk;e T[g:'rsk ;wheoD B{z fby'.

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