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I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34).
From (3.33),
LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}##
##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##
##=-\frac{u^2}{m}\frac{d^2u}{d\theta^2}-\frac{l^2u^3}{m}##
Multiplying throughout by ##-\frac{m}{l^2u^2}##, we have
LHS ##=\frac{1}{l^2}\frac{d^2u}{d\theta^2}+u##
which differs from (3.34).
What's wrong?
EDIT: I found the mistake. The text has a typo. The "1"s in (3.33) are actually "##l##"s.
From (3.33),
LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}##
##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##
##=-\frac{u^2}{m}\frac{d^2u}{d\theta^2}-\frac{l^2u^3}{m}##
Multiplying throughout by ##-\frac{m}{l^2u^2}##, we have
LHS ##=\frac{1}{l^2}\frac{d^2u}{d\theta^2}+u##
which differs from (3.34).
What's wrong?
EDIT: I found the mistake. The text has a typo. The "1"s in (3.33) are actually "##l##"s.
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