"...would have trouble imagining...": Is this present participle or gerund?

Given the sentence:

Most people who live and work near Washington, DC, would have trouble imagining dinosaurs walking around the area.

Grammatically, what would ‘imaging’ be called in this case? Present participle or gerund or something?

I mean, if it is a present participle, ‘imagining~’ might be a description of the subject. And if it is a gerund, ‘imagining~’ might be an object of the verb phrase of ‘have trouble’. How do they explain this ‘imagining’ after ‘have trouble’?

Solution 1:

1. Some verbs (other than auxiliaries) can take other verbs immediately after themselves:

She sat knitting.

He helped (to) wash up.

I enjoy imagining what it will be like when I'm old enough to ride free on the buses.

These constructions are known as catenations; notice that the second verb may be in the -ing form, the bare infinitive, or the to-infinitive. Behaviour of individual verbs varies.

2. Some multi-word constructions resemble single-word verbs both semantically

(put on a hat = don a hat

the aeroplane put down on the island = the aeroplane landed on the island

take place can = occur, happen)

and in where they can be used in larger structures (as these examples also show).

'Have trouble' is a multi-word verb that catenates with the -ing form of a verb (though I can't think of an exact single-word replacement). These are closely related expressions, though:

Ron had trouble passing his exams.

Hermione enjoyed taking her exams.

Hermione took pleasure in taking her exams.

Ron struggled to pass his exams.

George regretted failing his exams.

Fred avoided taking his exams.

The -ing forms used here (in five of the examples) are at the verb end of the verb–noun gradience: they are present participles.

According to 5 of the first 6 references I checked in a Google search for "gerund meaning", including the AHDEL and Collins, the -ing form used in the original example is NOT a gerund, though FumbleFingers' example would qualify. The treatment of the verbal–nounal gradience of -⁠ing forms found in Quirk et al shows that the term 'gerund' is probably best avoided. As my Google search indicates, it's not always used the same way anyway. If I was pressed, I'd say that (only) usage 2 below uses what most people would call a gerund:

1. Thieves stole a painting by Von Gaff yesterday. (deverbal noun)

2. Painting can be very therapeutic.

3. Leonardo was painting. (present participle)

4. Leonardo sat painting. (present participle)

5. Leonardo sat painting dinosaurs. (present participle)

6. Leonardo had trouble painting daleks. (present participle)

Solution 2:

Take the similar construction "In football, deliberately tripping an opponent is a foul"...

Here the verb trip occurs in its gerund form tripping, but this tripping is still a verb: it takes the adverb deliberately and the object an opponent. However, the entire phrase deliberately tripping an opponent, because of the gerund within it, now functions as a noun phrase, in this case as the subject of the sentence. So, a gerund is still a verb, but the phrase built around it is nominal, not verbal. [Source]

That may be a lot of cut & pasted material, but I think it's well put. The point it's irrelevant that the gerund can be further modified (by indirect objects, adverbs, etc.). Here's a link specifically dealing with to have trouble / problems verbing + ing / gerund.