I was wondering when eigenmodes (modes of vibration) were first mentioned in mechanics. Any reference would be appreciated.
I expect them to date back to the second half of the 19th century because of the breakthrough in linear algebras, but I'm not sure.
Additional notes This question was initially asked on physics.SE. I was suggested to post it here, but I'm keeping track of the comments below:
- [DanielSank] Fourier's big publication was 1822, and although the big example there was heat diffusion it definitely gets at the idea of normal modes. Interestingly, Wikipedia points out that decomposition into basis functions was kind of sort of known in antiquity, albeit without any true understanding of what was going on. But I don't think there was anything about vector space structure at that time some we can't speak "modal analysis", which is more general: any motion of a linear n-dimensional system (even non-periodic) can be decomposed as a linear combination of n modes.
- [CuriousOne] You may want to look at the references in Gram-Schmidt wiki. I think one should link an understanding of eigenmodes to an interest in orthogonalization of bases in linear spaces, which would put it formally closer to the end of the 19th, early 20th century. As it has been pointed out, these fairly trivial ideas have been invented multiple times, so it's not clear who was "first", since you have to pick based on the context.