Riemann Curvature Tensor

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In this video I show how the Riemann curvature tensor arises from the acceleration of the geodesic deviation vector.
Relevant videos:
Covariant derivative
• Riemann geometry -- co...
• A quick note on the co...
The geodesic equation
• The Geodesic Equation ...

Опубликовано:

16 сен 2024

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Комментарии : 28

@ausamahassan9559 5 лет назад

for step 2, 6:10, the fifth term misses (x-dot-j) in the christoffel term and is obvious from index balancethanks for reply if possible

@dXoverdteqprogress 5 лет назад

I had added anotations for both mistakes but for some reason RU-vid removed them. Thanks for pointing them out. I will pin this comment so others can see it.

@ausamahassan9559 5 лет назад

thanks a lot for your reply. and thanks again for the wonderful sincere presentation of all the beautiful lectures you delivered . I have followed literally all of them. I am holding masters in nuclear engineering but switched to physics lately as I always liked physics more!

@maheshudupa944 6 лет назад

Excellent explanation! I don’t understand how the views can be so less...

@ozzyfromspace 6 лет назад

Niche audience, that's all. His work's really good though; makes everything seem so much easier for the uninitiated, you know?

@ElliottCC 6 лет назад

I Love your videos....I love how technical they are. In my opinion, you should be the star of the internet

@dXoverdteqprogress 6 лет назад

Thanks! I appreciate that. I wish I had more time to continue making videos... Some day I will again. Cheers.

@ausamahassan9559 5 лет назад

at 7:13 the equation for geodesic deviation should read (d2(kai)/ds2) not (d(kai)/ds)and thanks for the wonderful presentation for all the videos

@tobiaszb 6 лет назад

Really like the explanation.

@signorellil 6 лет назад

I'm again a bit confused how the expansion at 05:21 was calculated. Can you explain please?

@revooshnoj4078 5 лет назад

Great intro!

@muntoonxt 7 лет назад

Music at the beginning is Tom Waits - Rain Dogs ;)

@dXoverdteqprogress 7 лет назад

It sure is.

@ozzyfromspace 6 лет назад

Another wonderful video! I don't have a university education so your lectures are really helping me out! Oh, and fantastic ending with the airplane flight attempts. I find aviation so fascinating, which just added to the allure of this presentation. Kudos, +dXoverdteqprogress. :)

@atzuras 3 года назад

this is gold

@earthperson79153 5 лет назад

Thanks. But also a bit confused about how the Xi shows up at in the xi double dot equation. And where do we find the table of contents of your lectures?

@BruceWayne-qj3nv 4 года назад

Can you please explain how did you cancel out the terms that were the derivative with respect to Chi at 5:20?

@veronicanoordzee6440 5 лет назад

After 5:14 you mention some kind of expansion. I see what happens, but I don't understand it. Can you give a link where this is explained? You mentioned it several times before.

@smokey04200420 3 года назад

Why would you turn off captions and not offer other solutions? I’m really interested in this, but I cannot understand what you say 2:59 “Euclidean geometry demands…” Can someone please tell me what he says?

@dXoverdteqprogress 3 года назад

"...that if two curves are geodesics, and they start out parallel to eah other, they must remain parallel for all time"

@maheshudupa944 7 лет назад

Why is this video unavailable? I was sort of looking forward for this!

@dXoverdteqprogress 7 лет назад

Hi, sorry about that -- if you're watching it on a phone, it might not show up due to copyright restrictions. You should be able to watch it on your PC; if not, let me know and I will post it on vidme etc. I will address your other comments tomorrow if you don't mind -- too tired. Cheers.

@davehumphreys1725 6 лет назад

Forgive me if I've missed something here, but I always thought that the 3 angles of a triangle, in Euclidean space, added up to 180 degrees. How on earth to they add up to pi?

@dXoverdteqprogress 6 лет назад

It is 180 degrees, but you can also express it in units called radians, in which 180 degrees = Pi radians and 360 degrees = 2Pi radians. Using radians makes is easy to compute arc lengths on a unit circle: Pi = half of circle; 2Pi full circle etc.

@davehumphreys1725 6 лет назад

I knew I'd missed something!! But, had you said, in your commentary, that the angles add up to pi RADIANS, instead of just saying that they add up to pi, which is just 3.14....I would have remembered. Do I have a point there?

@davehumphreys1725 6 лет назад

Ah! I knew I'd missed something. But, had you said in your commentary that the angles add up to pi RADIANS, instead of just saying that the add up to pi, which is just 3.14..... I would have remembered. Do I have a point here?