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I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the variable, something like:

$${\bf \hat{e} = \dfrac{e}{||e||} }$$

However, does the same apply to normalizing (and nondimensionalizing) a scalar? Would it be correct to write:

$$ \hat{L} = \dfrac{L}{L_0} $$

This is assuming that $L$ and $L_0$ are just scalar lengths. If I am defining my own notation, is it verboten to call this something like $\bar{L}$ (with a bar)?

If it makes any difference, I am a mechanical engineer and this will be going in my thesis.

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2 Answers

There is not, to my knowledge, a uniform standard on this subject. I have seen normalized quantities expressed by adding a twiddle (tilde) over the character (as in $\tilde{A}=A/A_0$), but I this notation is often reserved to indicate a time-varying quantity, instead. Unless someone knows of a strong standard in this regard, I'd say your best bet is to simply define the notation you will be using.

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I know in electrical engineering, particularly in power transmission fields, sometimes people use the so-called per-unit system, where quantities are normalized to the corresponding base value. Sometimes, subscript like $U_{\text{p.u.}}=\frac{U}{U_0}$ ($U_0=U_{\text{base}}$) is used. I don't think there are any proper notations for normalized scalars. You can follow the conventional notations in the particular area as long as there is no ambiguity.

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