Calculus of Variation

  • Thread starter Gavroy
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  • #1
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hey

I do not understand a step here!

The integral is:

[tex]\delta S(x,t)=-mc \int_a^b u_i d \delta x^i =0[/tex]

and now they say one should do integration by parts, but I do not know how this should work here?

Where are my two functions?As far as I see there is only the four-velocity and I do not how it depends on the differential so I wanted to ask you whether one of you could explain this step to me.

The result should be:

[tex]\delta S(x,t)=-mc u_i \delta x^i |^b_a + mc\int_a^b \delta x^i \frac{du_i}{ds} ds[/tex]

I have not a clue what happened there! Can you help me?
 

Answers and Replies

  • #2
fzero
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It's probably clearer if you write the original integral in longhand:

[tex]
\int_a^b u_i \frac{d (\delta x^i)}{ds} ds
[/tex]

The two functions are [tex]u_i[/tex] and [tex] \delta x^i[/tex].
 

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