Re: Help with Calculus of Variations Problem



David Rutherford wrote:

|\x=b x + yy'
| ----------------- dx
\|x=a (x^2 + y^2)^{3/2}

|\x=b d ( -1 )
= | -- (-----------------) dx
\|x=a dx ((x^2 + y^2)^(1/2))

|\x=b ( -1 )
= | d (-----------------)
\|x=a ((x^2 + y^2)^(1/2))

-1 |x=b
= ----------------- |
(x^2 + y^2)^(1/2) |x=a

1 1
= ---------------------- - ----------------------
(a^2 + (y(a))^2)^(1/2) (b^2 + (y(b))^2)^(1/2)

This didn't come out looking right, let me try again.

|\x=b x + yy'
| --------------- dx
\|x=a (x^2 + y^2)^(3/2)

|\x=b d ( -1 )
= | -- (---------------) dx
\|x=a dx ((x^2 + y^2)^(1/2))

|\x=b ( -1 )
= | d (---------------)
\|x=a ((x^2 + y^2)^(1/2))

-1 |x=b
= --------------- |
(x^2 + y^2)^(1/2) |x=a

1 1
= -------------------- - --------------------
(a^2 + (y(a))^2)^(1/2) (b^2 + (y(b))^2)^(1/2)


--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555

Applications:
"4/3 Problem Resolution"
"Action-reaction Paradox Resolution"
"Energy Density Correction"
"Proposed Quantum Mechanical Connection"
"Biot-Savart's Companion"

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