John,
   I would classify them as "absolutes", which I would define as subject
bearing participle clauses. (Traditional grammar calls them phrases.)
   My own preference would be for "he" and "I" in the subject roles, but
these are also commonly introduced by "with", which could be thought of
as understood here. "I slipped my backpack off, and we sat down at one
of the metal tables overlooking the pool, with him sipping his Mountain
Dew and me groping for pen and paper." Maybe the writer drafted it with
"with" and then took it out, leaving the objective pronouns.
   Hope that helps.

Craig
   >


What are the structures appended to the end of the main clause below?
> They
> feel like participles, but they have pseudo-subjects.  Is it correct to
> use
> the objective pronouns in these structures?
>
> *I slipped my backpack off, and we sat down at one of the metal tables
> overlooking the pool, him sipping his Mountain Dew and me groping for a
> pen
> and paper.
>
> *I hope everyone had a great Thanksgiving!
>
> Thanks,
> John
>
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