The Geodesic Equation (better sound quality) 

Cheers!

dXoverdteqprogress You are awesome ! thank you for this channel !

I like his videos too. But, don't forget, the real genius was EINSTEIN! Don't devaluate the term "genius", please. Reproducing the real thing is something else than producing it ;-)

I'm still mind blown by the clarity of your explanation... 5 hours later.

Back at it again, because your content gets clearer and clearer the more I watch it. It's essentially learning by reinforcement.

Thanks!

what about nongeodesics

Me too.

The metric g_ij depends on x(lambda); I added it in that step for clarity. I guess I should have stated it in the video.

Oh, that makes sense. Thank you.

I'm not sure I understand your question. We do integration by parts to turn chi dot into chi, which then allows us to factor it out.

@@dXoverdteqprogress I completed undergrad a couple years ago and apparently the integration in my head got rusty, I had to work it out on paper. I get it now! However, I'm curious why @5:08 we multiply by the inverse metric? thanks!

@@AllisinMusic Hi. We do so because we want to have only y double dot on the left hand side. Multiplying by the invers metric and summing over k gives y^q double dot.

@@dXoverdteqprogress Thanks so much for your quick response and of course these amazing and unique videos as well! Definitely helping prep for grad school! Blessings

Excellent. It's one of those things that are really simple once you work it out.

Can you explain it to me?

@@David-km2ie s(epsilon) = s(0) + epsilon s'(0) If s=sqrt(fgh), then the first derivative of s is D(sqrt(fgh))=[1/2 (fgh)^(-1/2)] (f' g h + f g' h + f g h') Yet I'm curious if I've gone wrong with the factor of 1/2, and whether that will make a difference in the final conclusions of the video.