Another example on how to calculate Christoffel symbols

This video uses one method to calculate the Christoffel symbols for spherical polar coordinate space. It uses the example of transforming from cartesian to spherical polar coordinates to show how basis vectors change from point to point in the space. This video is a follow up to a previous video which showed two methods for calculating these symbols and is entitled, ‘Calculating Christoffel symbols’.

[mdmehdihassan]

This video is disliked by none! Rare of a kind now a days in youtube 😂. Great video. Keep it on.

[thevegg]

Re the Christoffel symbols related to a curvilinear csys, the superscript on Gamma stands for the components of
the displacement vector, whose displacement is a comparison of the original vector (prior to transport) to the
vector's new position (after transport).

Are these components wrt the A) curvilinear csys or B) wrt to an orthographic csys?

I ask because its an easy task to find the components of a vector on an orthographic csys since there are many tick marks.
But on most graphic representations of curvilinear csyss, it's just four curves (not broken down into smaller units such
that one could measure the change in the displacement vect wrt to said curvilinear csys.

To me, that means that the breakdown of a displacement vector must be graphically calculated using an orthograhic cys
superimposede under the curvilinear one.

Are these components wrt the A) curvilinear csys or B) wrt to an orthographic csys?

[celsiusjunior]

Thanks to this video !! I understand the christofell symbols now !!!

[thevegg]

Thank you for your answer. I should say I’m no Einstein, lol, so I still have another question.
I’m assuming that the value of a particular Christoffel symbol may be the result of a measurement of the change of a basis vector dot producted with a vector that describes a change in angle after parallel transport.
Are you saying that if one were to try to represent this graphically, she would define the change directly on the curvy linear coordinate system. The type I’m thinking of can be very messy and irregular so how could it ever be possible to make a measurement of the change in a vector with respect to such cord system axis? I’m creating a graphic so the best I can do would be to somehow break the weird looking curvy linear square if you will with tick marks equally spaced. I did this and for one of the Christoffel symbols I got .3 in the X and .8 in the Y. These are the components that describe the difference vector in terms of the curvy linear coordinate system.
I guess my main question is does it sound reasonable to say that lambda bc, a is .3 in the x direction .8 in the y direction?
I have created a graphic that will clearly fine the question. If you would be so kind to email me, I will send you a JPEG of the image. I’m trying to define one image that explains Christoffel symbols, visually and clearly hopefully for the benefit of others as well as myself

[Scientificirfann]

Can I get its pdf if available?😍 The video is just awesome

[divyakulkarni]

Firstly thanks a lot sir!
Will you plz explain here that how to find Ricci tensor and ricchi scalar for sphere?

[dariocampos]

Great video, thanks!

7:15 I've been struggling with that specific part, how to get cos(theta) / sin(theta) * e_phi. I keep getting r*cos(theta)*e_phi.

Could you, please, elaborate on that? Thanks!

[ThurVal]

I am still confused .. how does the full matrix look like? The base-vector-tupel is already a matrix, the contras too plus another direction by derivatives..