A poem was written by David to explain the nature of love. And this poem attracted me. Can I write this?
The poem written by David explaining love attracted me.
Let's imagine a poem has been written on a signboard in a park, and this poem explains the nature of love. Can I write this?
The poem written on the signboard in this park explaining love attracted me.
This would be easier explained with a sentence diagram.
"The poem written by David explaining love" is a noun phrase that acts as the subject of the sentence.
This phrase is made up of a noun phrase and a participle clause: "The poem written by David" + "explaining love"
This noun phrase is in turn made up of "The poem" and the adjectival phrase "written by David".
This is perfectly grammatical, but this kind of construction is considered bad form because it makes the sentence harder to read. It can be 'fixed up' to make it more readable: "The poem explaining love, written by David, attracted me." The change in order is because "the poem" and "David" are both capable of "explaining", so it's ambiguous. It's clear that "the poem" and not "love" was "written". The parenthetical commas break up the sentence so it's easier to parse.
These sentences are entirely proper, although as Nazmul Hassan suggests you would do better to rephrase them so it is clearer what the explaining clause modifies.
Don't be misled by the traditional names present participle and past participle. Participles don't have tense; the clauses they head "borrow" their tenses from the surrounding context. You would do better to think of these as active and passive participles or as perfect and progressive participles.
