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The phrase "a second variation of" is correct and usable in written English.
It can be used when discussing different forms or versions of something, indicating that it is the second in a series of variations.
Example: "In this study, we will explore a second variation of the original experiment to see if the results differ."
Alternatives: "an alternative version of" or "a different iteration of".
Exact(1)
The quadratic functional (2) defined over various classes of admissible functions is studied extensively in the literature because of the connection with the second variation: (2) is a second variation of the functional K ( x 0, x N + 1 ) + ∑ k = 0 N g ( k, x k + 1, Δ x k ), see [4] for details.
Similar(59)
A first variation of the discrete model we discussed in Sect.
However, a third variation of the basic model is the presence of an oligomeric intermediate (Eq. 5).
On the basis of our inference in this study, we suggest a third variation of acetabular ossification in DDH that is not visible in childhood but is manifest in adolescence as an upward tilt of the outer portion of the acetabular rim.
IF PALLETT AND CLARK ACHIEVE POP liberation through technology, "chops" and a flair for performance, a third variation on the theme of musical self-sufficiency is presented by the curious case of Noah Lennox.
A positive definite second variation of the total energy is used as a sufficient criterion for stability of equilibrium configurations.
We have proved that in the former case, subject to a smallness condition, the second variation of the energy is strictly positive at these whirling solutions and hence that the latter solutions are stable.
It is the second variation of a series, of which another work, "Personnes," will be on view from mid-January to mid-February at the Grand Palais in Paris.
Or more accurately, a third variation is winning — a combination of the two.
A third variation was written during the night of 21 February 1818.
Specifically, by setting the action's first and second frequency derivatives equal to zero it is shown that, all along the FEC, both the first and second derivatives of the load with respect to the frequency keep a strict negative sign; these action derivatives are special cases of the general first and second variations of a variable endpoints variational problem.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com