A decent explanation is here:
<a href="http:&#x2F;&#x2F;www.physicspages.com&#x2F;2013&#x2F;03&#x2F;30&#x2F;geodesics-paths-of-longest-proper-time&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.physicspages.com&#x2F;2013&#x2F;03&#x2F;30&#x2F;geodesics-paths-of-lo...</a>
(I haven&#x27;t checked all the calculations though).
A similar explanation is shown in Feynman&#x27;s lectures:<a href="http:&#x2F;&#x2F;www.feynmanlectures.caltech.edu&#x2F;II_42.html" rel="nofollow">http:&#x2F;&#x2F;www.feynmanlectures.caltech.edu&#x2F;II_42.html</a>