Grammatical Structure Problem

[Deepurple]

"With these hopes and in this belief I would urge you, laying aside all hindrance, thrusting away all private aims, to devote yourselves unswervingly and unflinchingly to the vigorous and successful prosecution of this war."

I would like to know what the grammatical structure of the underlined expression is. Does it modify the object "you" in the sentence? What function of such a clause is used for?

Thank you.

[colloquium]

It seems to me that the underlined section modifies the verb devote.

However I am not entirely sure.

I am not a teacher.