- #1
Philip Koeck
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- 204
I have an analytical function F of the discrete variables ni, which are natural numbers. I also know that the sum of all ni is constant and equal to N.
N also appears explicitly in F, but F is not a function of N. F exists in a coordinate system given by the ni only.
Should I carry out the variation as if N would vary when I vary any of the ni and then apply the constant N as a constraint with a Lagrange multiplier or is it correct to leave out the variation of N with ni from the beginning.
As an example you can look at: F = N + ∑gi ln ni
The gi are just weights, which can be different for every i.
N also appears explicitly in F, but F is not a function of N. F exists in a coordinate system given by the ni only.
Should I carry out the variation as if N would vary when I vary any of the ni and then apply the constant N as a constraint with a Lagrange multiplier or is it correct to leave out the variation of N with ni from the beginning.
As an example you can look at: F = N + ∑gi ln ni
The gi are just weights, which can be different for every i.
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