- #1
binbagsss
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Homework Statement
##J=r^{2}\dot{\phi}## [1]
##\dot{r^{2}}=E^{2}-1-\frac{J^{2}}{r^{2}}+\frac{2MJ^{2}}{r^{3}}+\frac{2M}{r}##. [2]
(the context is geodesic equation GR, but I'm pretty sure this is irrelevant).
where ##u=r^{-1}##
Question: From these two equations to derive ##(\frac{du}{d\phi})^{2}=\frac{1}{J^{2}}(E^{2}-1-\frac{J^{2}}{r^{2}}+\frac{2MJ^{2}}{r^{3}}+\frac{2M}{r})##
Homework Equations
As above.
The Attempt at a Solution
[/B]
I know that ##(\frac{du}{d\phi})^{2}=(\frac{\dot{u^{2}}}{\dot{\phi^{2}})}##.
The ##J^{2}## in the denominator is throwing me, I see from [1] that ##\dot{\phi}=Jr^{-2}## so there's some relation between ##\dot{\phi}## and ##J##, but what about a ## r^{-4}## term with the ##J^{2}##, since the long term in brackets remains from [2].
I'm guessing I'm missing something simple but I've spent a long time looking at it and no luck.
Cheers.
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