- #1

LagrangeEuler

- 701

- 19

##δI=δ^2I=0##. Then I must go with finding further variations. And if ##δ^3I>0## is then that minimum? Or what?

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- Thread starter LagrangeEuler
- Start date

- #1

LagrangeEuler

- 701

- 19

##δI=δ^2I=0##. Then I must go with finding further variations. And if ##δ^3I>0## is then that minimum? Or what?

- #2

muzialis

- 166

- 1

The stationarity of the functional, i.e. δI=0 , occurs for maxima, minima and saddles.

- #3

LagrangeEuler

- 701

- 19

So then how I could know? Is it minimum or maximum?

- #4

muzialis

- 166

- 1

If you have the book "introduction to Calculus of Variations" by Fox you will find there a thorough discussion of the second variation: yes further variations are to be computed.

I really do apologise for my previous reply which was wildly inaccurate due to a misunderstanding of mine.

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