I'm looking at equation (41) from equation (40) on http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken] and the second term, it says that these equations are given up to ##O(\epsilon)##.(adsbygoogle = window.adsbygoogle || []).push({});

Looking at equation (32) for ##g_{00}## I see it is proportional to ##\Phi##, and from looking at (31) I see that ##\Phi ## is of the same order as ##d^{2}x^{i}/dt^{2}## .

Looking at the 2nd term in (41) which has only been multiplied by a ##-1## from the ##g_{00}## I conclude that it is only possible to be given up to ##O(\epsilon)## if ##\Phi## , and so, ## d^{2}x^{i}/dt^{2}##, is of the order ##O(\epsilon^{2})##

By definition of the slow approximation we have ##dx^{i}/dt=O(\epsilon)##. And time derivatives are neglected compared to space derivatives.

It seems to me quite possible that ##d^{2}x^{i}/dt^{2}## being of the order ##O(\epsilon^{2})## can be justified.

However I'm not sure how to show this properly/explicitly?

Thanks.

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# Slow motion approx, order of acceleration quick Q?

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