What is the purpose of this Mizmor?
Radak: Many of these Mizmorim are to strengthen the hearts of people despairing from Ge'ulah due to the length of Galus.
Why does it say "Hashem Malach"?
Rashi: This is after kingship was taken from Amalek.
Why does it say "Tagel ha'Aretz"?
Rashi: This is like "ki'Smo'ach Kol ha'Aretz Shemamah E'eseh Lach" (Yechezkel 35:14); it is a Nevu'ah about Amalek.
Malbim: Via Hashem's kingship in this way - Hashgachah via nature - the land will have Gilah, i.e. Simchah over a new matter. A new conduct of the land will agree with Hashem's intent for reward and punishment.
Why does it say "Yismechu Iyim Rabim"?
Malbim: Even though there will be a Chidush, that nature will need to agree with reward and punishment (to which Gilah applies), in parts of the land and some islands 1 there will be constant Simchah, for nature will not change in details, rather, in general. This is the difference between revealed miraculous Hashgachah which the coming Mizmorim discuss, and Hashgachah via nature that this Mizmor discusses. In miraculous Hashgachah, also details change. The miracle is for one person or one nation. In Hashgachah via nature, nature in general is according to reward or punishment, e.g. rain will be based on what the world deserves. Some think that this is natural and inevitable, so they feel Simchah.
I do not understand why the verse mentions specifically islands. (PF)
