This question may be too academic for this place but I'll give it a go anyway and hopefully, some can help clarify this
I read several books on phonetics and phonology and can summarize that coarticulation consists of double articulation [e.g. /w/ in English] and a pair of 'primary and secondary articulation' [e.g. a labialized s, as in /s/ in sweet]. However, I really don't quite understand why nasalized vowels are classified as coarticulation as well. The lowering and raising of the velum isn't really a stricture to consider. Can someone please help clarify this? Thanks a lot
Coarticulation occurs because the different speech production processes, and the different articulators involved, combine with one another with different timing patterns. For example, vowels become nasalized when followed (or preceded) by a nasal consonant (compare English "pit" and "pin") because the timing of the lowering of the velum is not perfectly synchronized with the tongue movement for the alveolar consonant.
The word “Coarticulation” has more than one definition and many phoneticians (for example, Peter Ladefoged, Michael Ashby, Peter Roach, and so on) define it differently from yours. Probably the most common definition of “coarticulation” is something like this: The articulatory overlapping of adjacent sounds (unlike the common definition of “secondary articulation,” it is not limited only to the oral stricture of open approximation like labialization, palatalization, or velarization). And if you go by this definition, English nasalized vowels and a labialized /s/ in “sweet” are perfect examples of coarticulation, but on the other hand, English /w/ and French nasal vowels are not, because their articulatory gestures are inherent; in other words, they are not influenced by their adjacent sounds. So, whether English nasalized vowels should be classified as coarticulation or not simply depends on how you define “coarticulation.”