Talk:Harmonic balance

Possible misattribution
The article starts out saying, that the Harmonic Balance methods was originally introduced by Michel Nahkla. Looking at the given reference however, in the paper's introduction one can find: "..., the harmonic balance method as originally implemented by Baily and Lindenlaub ...".

Being newly registered I want to ask for advice, if and how this should be corrected. Standing on its own, it looks like a mis-attribution of the method. It is particularly curious because the change adding this attribution was done by a user Mikey1720, who has also added some curiously flattering words to the article about Michel Nakhla, and didn't make much of other contributions to Wikipedia, making it look a lot like an edit by the author himself.

--Editeditit (talk) 10:11, 29 September 2021 (UTC)

Possibly overly specific
Additionally, literature seems to use the terminology of "harmonic balance" or "balancing the harmonics" in a more general sense:

Given an equation

F(t,x(t),\dot x(t)) = 0 $$ that has been rewritten in terms of coefficients $$x_k$$ as

\sum_j F_j(\{x_k\}) e^{i\omega(j) t} = 0, $$ where any number of terms $$F_j$$ may have the same frequency $$\omega(j)$$.

Be $$\{\omega_k\}$$ the set of unique frequencies appearing above.

Then the terminology "balancing the harmonics" or "harmonic balance" is used to describe the two steps of using linear-independence of the functions $$e^{i\omega_k t}$$ to (a) group terms with equal frequencies $$\omega_k$$ together into a single expression

\sum_j^{\omega(j)=\omega_k} \left(     F_j(\{x_{k'}\})    \right) e^{i\omega_k t} $$ and (b) set the time-independent part of each expression equal to zero, thereby obtaining an equation system

\sum_j^{\omega(j)=\omega_k} F_j(\{x_{k'}\}) = 0 \qquad \forall  \omega_k. $$

One example of such usage of the terminology is this lecture, but also the way the terminology is used by Nakhla and Vlach. I didn't have access to their references by Baily and Lindenlaub, so I couldn't yet find earlier mentions of the "harmonic balance" terminology.

Additionally, the equivalent German terminology of "Harmonische Balance" seems to be used quite differently. I wasn't yet able to verify how strongly the articles are related.

--Editeditit (talk) 13:21, 1 October 2021 (UTC)