What is “normal” about normal frequencies and normal modes?

[AntonPannekoek]

So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.

 

[andrewkirk]

I don't know the etymology of the term, but 'normal' as 'orthogonal' would certainly work, because the normal modes correspond to eigenvectors of a matrix, and those eigenvectors will be orthogonal to one another.
'Normal coordinates' in Differential Geometry are coordinates that give a locally orthogonal basis, so 'normal coordinates' could also be based on 'orthogonal'.

 

[spareine]

The original meaning is perpendicular. In classical Latin normalis was a carpenter's square, and the word was also used for rectangular shapes made according to the carpenter's square. In Late Latin (in the early middle ages) it could mean perpendicular, or regular, in conformity with rule. The modern meaning of 'usual state or condition' (without explicit rules) seems to have developed in the 19th century. (See dictionary)

 

[marcusl]

In English works they were often referred to as "characteristic modes," which I think describes their role well. The German words eventually too over.

 

[spareine]

"Normal" in the "normal distribution" may need some clarification as well. Gauss himself coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual". However, by the end of the 19th century some authors started stating that this distribution was typical, common – and thus "normal". (wikipedia)