Geodesics

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Hastings

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Can anyone help me through this question? Thanks
 

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Hastings said:
Can anyone help me through this question? Thanks
Click to expand...
Can't read the jpeg file - 514×244 is not enough pixels to be legible.

Also - we need to see your work!

EDIT: no change in resolution with your second try - just narrower margins. Can't tell difference between "a" and "alpha," for instance.
 
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Hello. Can you explain how to find the first variation formula for E ? For the second I let
Code: 
F(s,t)=a_{s}(t)
be a smooth variation and I think I can probably show E is constant by showing it's derivative is zero.
 
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The picture's better now. Can anyone tell me how to find the first variation formula?
 
Subhotosh Khan said:

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")
Click to expand...

I completely understand and indeed (mostly) agree with your philosophy on teaching maths. If you could just tell me how to find the first variation formula, I will endeavour to find it for myself. I have never heard of this concept.
 
Hastings said:
I completely understand and indeed (mostly) agree with your philosophy on teaching maths. If you could just tell me how to find the first variation formula, I will endeavour to find it for myself. I have never heard of this concept.
Click to expand...

Are you taking a course in Variational Calculus?

This is an advanced topic - the whole subject of finite element analysis in structural mechanics is based on this principle.

Self study in this topic can be very difficult (at least for me) but you can start with a Google search - start with the article by Prof. Olver and then the article in wolfram and work through the rest.

http://www.math.umn.edu/~olver/am_/cvz.pdf

http://mathworld.wolfram.com/CalculusofVariations.html

http://en.wikipedia.org/wiki/Calculus_of_variations
 
I am studying differential geometry Where can I find how to do question (i). Do you know how to do it. Just give me the hints your scruples will allow.
 
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