I am just wondering what is the connection between parameter space and configuration space (or phase space)? I know the connection between configuration space and phase space but it seems like any paper/source I see uses one of "parameter space" or "configuration space" but I see no where is it explicitly stated whether or not the two are the same or the relationship between them if they are different.
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My understanding is that "parameter space" is a generic name that could apply for both configuration and phase space (or really any other kind), while configuration space exclusively refers to the space of the genealised coordinates. It might be the case that authors tend to avoid refering to phase space as "parameter space" while not doing the same for configuration space, perhaps because phase space is more often utilised.
