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I'm writing an engineering paper which is filled with equations (physical demonstrations in the theoretical section and numerical methods demonstrations in the methods section).

I want to rewrite one of the first equation I introduced, because I introduced it in a particular context and now I want to use it in another context and show different properties of it. Is this considered a bad practice?

Since all equations are numbered, there would be an equation which is numbered twice. I could solve this problem by not numbering just the second appearance of this equation. Or I could just reference the number, and let the reader go back a few pages. But that would affect the readability of the text (all the other instances in which I reference some previous equation are usually in the same paragraph, so there's no need to turn a lot of pages).

What should I do? Redundancy and readability or conciseness and elegance in spite of readability?

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    It would help to know the length of the paper, and the number of equations you might want to repeat. Looking back four pages is not the same a look back forty pages.
    – Terry Loring
    Commented Mar 10, 2021 at 19:34
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    Amplifying what Terry Loring said: If it is a document broken into chapters with quite different topics, it is more likely to repeat an equation. A book, a long survey report, a PhD thesis, etc., are good candidates. If it's a research article with one main topic, it is less likely to require repeats.
    – puppetsock
    Commented Mar 11, 2021 at 14:50

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I'd suggest just referencing the previous entry. People reading technical articles are pretty used to skipping back if necessary. It might be confusing to repeat it with a new number, especially.

An alternative would be to repeat it along with the original number, making a note of what you are doing:

...repeating equation (42) x = y + z...

But the reference to the equation is likely enough.

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In general, I think “readability” is overrated in technical material. You should absolutely try to be as clear as possible, but repeating an equation is a micro-optimization that saves the reader only a few seconds. Remember that the vast majority of readers are not even going to read the technical content, while those that want to understand it in detail will spend much longer on the paper. Properly understanding a bunch of equations can take hours, so making the set of equations longer just to save the reader a few seconds on the first skim seems counterproductive.

A better solution is to describe the equation qualitatively, such as “In this context, the dissipation equation (45) implies...” This helps the reader by giving context.

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  • Indeed, and being sure to name it "the dissipation equation" (etc.) at its first occurrence. Descriptive names are much better than purely artifactual numbers.
    – paul garrett
    Commented Mar 10, 2021 at 18:54
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    repeating an equation is a micro-optimization that saves the reader only a few seconds If only. Time is not the only thing you can optimize for. There's plenty enough out there to suggest that locality of reference helps in both understanding and retention of the material, at least in the earliest stages of knowledge acquisition, i.e. when it's all new to the reader. Repetitions that improve locality of reference are hardly a micro optimization: their absence is a premature pessimization hell bent on file sizes (i.e.: who cares!) with no regard for human consumers of this knowledge.
    – Kuba hasn't forgotten Monica
    Commented Mar 10, 2021 at 23:51
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Do as you please, just be clear as to what you're doing. E.g.,

We rewrite Equation (1) by x, y, and z:

... (1a)

Because a, b, and c.

In the example, the goal is to make it clear to the reader that an earlier equation is being rewritten and the reasons why it is being rewritten. I've labelled (1a) to show a relation with (1). Perhaps the label isn't necessary, it depends whether you want to refer back to (1a) having introduced it (or you think others might want to refer to it).

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